mounir hsini - Academia.edu (original) (raw)

Papers by mounir hsini

Complex Analysis and Operator Theory, 2019

The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ... more The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ⎨ ⎪ ⎩ M × |u(x)−u(y)| p(x,y) p(x,y)|x−y| N + p(x,y)s dxdy () s p(x,.) u(x) = λ f (x, u) − |u(x)| q(x)−2 u(x) in , u = 0 in ∂ , where ⊂ R N , N ≥ 2 is a bounded smooth domain, M and f are two continuous functions and () s p(.,.) is the fractional p(., .)-Laplacian while λ is a positive parameter and 0 < s < 1. Using variational techniques combined with the theory of the generalized Lebesgue Sobolev spaces, we prove some existence and multiplicity results for the problem in an appropriate space of functions.

Journal of Elliptic and Parabolic Equations

Communications on Applied Electronics, 2015

Long Term Evolution (LTE) is an advanced standard of the mobile communication systems. LTE has be... more Long Term Evolution (LTE) is an advanced standard of the mobile communication systems. LTE has been developed by the 3 rd Generation Partnership Project (3GPP). The new features exhibited by LTE is a direct impact of applying new modulation and coding techniques such as the Orthogonal Frequency Division Multiplexing (OFDM) for the Downlink and the Single Carrier Frequency Division Multiple Access (SC-FDMA) for the Uplink as well as turbo coding. This paper presents a Field Programmable Gate Array (FPGA) design and implementation of the LTE downlink transmitter and receiver according to releases 8 and 9 on Virtex 6 XC6VLX240T FPGA kit using Xilinx® ISE® Design Suite version 12.1. It is found that the utilization of the look up tables and flip plops amounts to about 65 percent while the other logic devices utilization on the chip amount to only 5-13 percent. Such implementations can be considered as IPs for software defined radios. The information is also useful for the FPGA developers. The most important consequence is that the FPGA vendors may produce more appropriate counts of the resource blocks for better the utilization of the chips used in the LTE transceivers.

Complex Analysis and Operator Theory, 2019

The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ... more The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ⎨ ⎪ ⎩ M × |u(x)−u(y)| p(x,y) p(x,y)|x−y| N + p(x,y)s dxdy () s p(x,.) u(x) = λ f (x, u) − |u(x)| q(x)−2 u(x) in , u = 0 in ∂ , where ⊂ R N , N ≥ 2 is a bounded smooth domain, M and f are two continuous functions and () s p(.,.) is the fractional p(., .)-Laplacian while λ is a positive parameter and 0 < s < 1. Using variational techniques combined with the theory of the generalized Lebesgue Sobolev spaces, we prove some existence and multiplicity results for the problem in an appropriate space of functions.

arXiv: Analysis of PDEs, 2009

In this paper, we prove the existence of weak solutions for the following nonlinear elliptic syst... more In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system {lll} -\\Delta_{p(x)}u = a(x)|u|^{p(x)-2}u - b(x)|u|^{\\alpha(x)}|v|^{\\beta(x)} v + f(x) in \\Omega, \\Delta_{q(x)}v = c(x) |v|^{q(x)-2}v - d(x)|v|^{\\beta(x)}|u|^{\\alpha(x)} u + g(x) in \\Omega, u = v = 0 \\quad on \\partial\\Omega, where Omega\\OmegaOmega is an open bounded domains of mathbbRN\\mathbb{R}^NmathbbRN with a smooth boundary partialOmega\\partial\\OmegapartialOmega and Deltap(x)\\Delta_{p(x)}Deltap(x) denotes the p(x)p(x)p(x)-Laplacian.The existence of weak solutions is proved using the theory of monotone operators. Similar result will be proved when Omega=mathbbRN\\Omega=\\mathbb{R}^NOmega=mathbbRN.

The purpose of this work is to study the following singular problem: [Formula: see text] where [F... more The purpose of this work is to study the following singular problem: [Formula: see text] where [Formula: see text], [Formula: see text] be a bounded smooth domain, [Formula: see text] is a positive parameter, [Formula: see text] such that [Formula: see text] and [Formula: see text], [Formula: see text] where [Formula: see text] We employ the Nehari manifold approach and the fibering maps in order to show the existence of [Formula: see text] such that for all [Formula: see text], problem [Formula: see text] has at least two solutions.

In this paper, we study the fractional p(x)-Laplacian problem with variable exponents  (−∆)p(... more In this paper, we study the fractional p(x)-Laplacian problem with variable exponents  (−∆)p(.)u(x)+ |u(x)| q(x)−2u(x) = λ ∂F ∂u (x,u), x ∈Ω, u(x) = 0, x ∈ ∂Ω. Where Ω ⊂ RN , N > 2 is a bounded smooth domain, F ∈ C1(Ω×R,R) while λ is a positive parameter and q is a continuous function on Ω.

Journal of Applied Analysis & Computation

Journal of Physical Mathematics

In this paper, we investigate the parabolic logistic equation with blow-up initial and boundary v... more In this paper, we investigate the parabolic logistic equation with blow-up initial and boundary values on a smooth bounded domain where T>0. Under suitable assumptions on a(x, t) and f, we show that such solution stays bounded in any compact subset of Ω as t increase to T. Other asymptotic estimates will given in this work.

Applicable Analysis

In this paper, we consider for a given smooth bounded domain Ω of , the following -biharmonic typ... more In this paper, we consider for a given smooth bounded domain Ω of , the following -biharmonic type problem where λ is a positive parameter, with ξ is a function which satisfies the condition with and is a function. We prove the existence of a continuous family of eigenvalues in a neighbourhood of the origin, under some suitable conditions by using Ekeland's principle and variational method.

Rocky Mountain Journal of Mathematics

In this paper, we prove the existence of weak solutions for the following nonlinear elliptic syst... more In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system −div A(x, ∇u) = −a(x)|u| p(x)−2 u − b(x)|u| α(x) |v| β(x) v + f (x) in Ω, −div B(x, ∇v) = −c(x)|v| q(x)−2 v − d(x)|v| β(x) |u| α(x) u + g(x) in Ω, u = v = 0 on ∂Ω, where Ω is an open bounded domains of R N with a smooth boundary ∂Ω. The existence of weak solutions is proved using the theory of monotone operators.

This paper is concerned with the existence theory of a semilinear elliptic system. In particular,... more This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we prove that the system has a nontrivial positive solution in some appropriate solution spaces.

Complex Variables and Elliptic Equations

ABSTRACT This paper is concerned with a weighted Steklov problem involving the -Laplacian operato... more ABSTRACT This paper is concerned with a weighted Steklov problem involving the -Laplacian operator in Sobolev spaces with variable exponents Our approach is based on variational method and Ekeland's principle, we establish that the above problem admits a nontrivial weak solution under appropriate conditions.

e.ijpam.eu

The goal of this paper is to study the properties of solutions of ∆u + f 1 (u) − f 2 (u) = 0 in a... more The goal of this paper is to study the properties of solutions of ∆u + f 1 (u) − f 2 (u) = 0 in all of R n . We obtain Liouville type boundedness results for the solutions. We show that either u is bounded on R n if it changes sign or u is a constant if it does not change sign.

Arxiv preprint arXiv:0902.2507, Jan 1, 2009

In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system

Annals of the University of Craiova-Mathematics and …, Jan 1, 2009

ams.org

We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result... more We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result which obtained by the method of moving planes with an improved Aleksandrov-Bakelman-Pucci (ABP) type estimate for the fractional Laplacian in unbounded domain.

We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result... more We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result which obtained by the method of moving planes with an improved Aleksandrov-Bakelman-Pucci (ABP) type estimate for the fractional Laplacian in unbounded domain.

Complex Analysis and Operator Theory, 2019

The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ... more The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ⎨ ⎪ ⎩ M × |u(x)−u(y)| p(x,y) p(x,y)|x−y| N + p(x,y)s dxdy () s p(x,.) u(x) = λ f (x, u) − |u(x)| q(x)−2 u(x) in , u = 0 in ∂ , where ⊂ R N , N ≥ 2 is a bounded smooth domain, M and f are two continuous functions and () s p(.,.) is the fractional p(., .)-Laplacian while λ is a positive parameter and 0 < s < 1. Using variational techniques combined with the theory of the generalized Lebesgue Sobolev spaces, we prove some existence and multiplicity results for the problem in an appropriate space of functions.

Journal of Elliptic and Parabolic Equations

Communications on Applied Electronics, 2015

Long Term Evolution (LTE) is an advanced standard of the mobile communication systems. LTE has be... more Long Term Evolution (LTE) is an advanced standard of the mobile communication systems. LTE has been developed by the 3 rd Generation Partnership Project (3GPP). The new features exhibited by LTE is a direct impact of applying new modulation and coding techniques such as the Orthogonal Frequency Division Multiplexing (OFDM) for the Downlink and the Single Carrier Frequency Division Multiple Access (SC-FDMA) for the Uplink as well as turbo coding. This paper presents a Field Programmable Gate Array (FPGA) design and implementation of the LTE downlink transmitter and receiver according to releases 8 and 9 on Virtex 6 XC6VLX240T FPGA kit using Xilinx® ISE® Design Suite version 12.1. It is found that the utilization of the look up tables and flip plops amounts to about 65 percent while the other logic devices utilization on the chip amount to only 5-13 percent. Such implementations can be considered as IPs for software defined radios. The information is also useful for the FPGA developers. The most important consequence is that the FPGA vendors may produce more appropriate counts of the resource blocks for better the utilization of the chips used in the LTE transceivers.

Complex Analysis and Operator Theory, 2019

The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ... more The aim of this paper is to study the existence of nontrivial weak solutions for the problem ⎧ ⎪ ⎨ ⎪ ⎩ M × |u(x)−u(y)| p(x,y) p(x,y)|x−y| N + p(x,y)s dxdy () s p(x,.) u(x) = λ f (x, u) − |u(x)| q(x)−2 u(x) in , u = 0 in ∂ , where ⊂ R N , N ≥ 2 is a bounded smooth domain, M and f are two continuous functions and () s p(.,.) is the fractional p(., .)-Laplacian while λ is a positive parameter and 0 < s < 1. Using variational techniques combined with the theory of the generalized Lebesgue Sobolev spaces, we prove some existence and multiplicity results for the problem in an appropriate space of functions.

arXiv: Analysis of PDEs, 2009

In this paper, we prove the existence of weak solutions for the following nonlinear elliptic syst... more In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system {lll} -\\Delta_{p(x)}u = a(x)|u|^{p(x)-2}u - b(x)|u|^{\\alpha(x)}|v|^{\\beta(x)} v + f(x) in \\Omega, \\Delta_{q(x)}v = c(x) |v|^{q(x)-2}v - d(x)|v|^{\\beta(x)}|u|^{\\alpha(x)} u + g(x) in \\Omega, u = v = 0 \\quad on \\partial\\Omega, where Omega\\OmegaOmega is an open bounded domains of mathbbRN\\mathbb{R}^NmathbbRN with a smooth boundary partialOmega\\partial\\OmegapartialOmega and Deltap(x)\\Delta_{p(x)}Deltap(x) denotes the p(x)p(x)p(x)-Laplacian.The existence of weak solutions is proved using the theory of monotone operators. Similar result will be proved when Omega=mathbbRN\\Omega=\\mathbb{R}^NOmega=mathbbRN.

The purpose of this work is to study the following singular problem: [Formula: see text] where [F... more The purpose of this work is to study the following singular problem: [Formula: see text] where [Formula: see text], [Formula: see text] be a bounded smooth domain, [Formula: see text] is a positive parameter, [Formula: see text] such that [Formula: see text] and [Formula: see text], [Formula: see text] where [Formula: see text] We employ the Nehari manifold approach and the fibering maps in order to show the existence of [Formula: see text] such that for all [Formula: see text], problem [Formula: see text] has at least two solutions.

In this paper, we study the fractional p(x)-Laplacian problem with variable exponents  (−∆)p(... more In this paper, we study the fractional p(x)-Laplacian problem with variable exponents  (−∆)p(.)u(x)+ |u(x)| q(x)−2u(x) = λ ∂F ∂u (x,u), x ∈Ω, u(x) = 0, x ∈ ∂Ω. Where Ω ⊂ RN , N > 2 is a bounded smooth domain, F ∈ C1(Ω×R,R) while λ is a positive parameter and q is a continuous function on Ω.

Journal of Applied Analysis & Computation

Journal of Physical Mathematics

In this paper, we investigate the parabolic logistic equation with blow-up initial and boundary v... more In this paper, we investigate the parabolic logistic equation with blow-up initial and boundary values on a smooth bounded domain where T>0. Under suitable assumptions on a(x, t) and f, we show that such solution stays bounded in any compact subset of Ω as t increase to T. Other asymptotic estimates will given in this work.

Applicable Analysis

In this paper, we consider for a given smooth bounded domain Ω of , the following -biharmonic typ... more In this paper, we consider for a given smooth bounded domain Ω of , the following -biharmonic type problem where λ is a positive parameter, with ξ is a function which satisfies the condition with and is a function. We prove the existence of a continuous family of eigenvalues in a neighbourhood of the origin, under some suitable conditions by using Ekeland's principle and variational method.

Rocky Mountain Journal of Mathematics

In this paper, we prove the existence of weak solutions for the following nonlinear elliptic syst... more In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system −div A(x, ∇u) = −a(x)|u| p(x)−2 u − b(x)|u| α(x) |v| β(x) v + f (x) in Ω, −div B(x, ∇v) = −c(x)|v| q(x)−2 v − d(x)|v| β(x) |u| α(x) u + g(x) in Ω, u = v = 0 on ∂Ω, where Ω is an open bounded domains of R N with a smooth boundary ∂Ω. The existence of weak solutions is proved using the theory of monotone operators.

This paper is concerned with the existence theory of a semilinear elliptic system. In particular,... more This paper is concerned with the existence theory of a semilinear elliptic system. In particular, we prove that the system has a nontrivial positive solution in some appropriate solution spaces.

Complex Variables and Elliptic Equations

ABSTRACT This paper is concerned with a weighted Steklov problem involving the -Laplacian operato... more ABSTRACT This paper is concerned with a weighted Steklov problem involving the -Laplacian operator in Sobolev spaces with variable exponents Our approach is based on variational method and Ekeland's principle, we establish that the above problem admits a nontrivial weak solution under appropriate conditions.

e.ijpam.eu

The goal of this paper is to study the properties of solutions of ∆u + f 1 (u) − f 2 (u) = 0 in a... more The goal of this paper is to study the properties of solutions of ∆u + f 1 (u) − f 2 (u) = 0 in all of R n . We obtain Liouville type boundedness results for the solutions. We show that either u is bounded on R n if it changes sign or u is a constant if it does not change sign.

Arxiv preprint arXiv:0902.2507, Jan 1, 2009

In this paper, we prove the existence of weak solutions for the following nonlinear elliptic system

Annals of the University of Craiova-Mathematics and …, Jan 1, 2009

ams.org

We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result... more We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result which obtained by the method of moving planes with an improved Aleksandrov-Bakelman-Pucci (ABP) type estimate for the fractional Laplacian in unbounded domain.

We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result... more We study the nonexistence of solutions for fractional elliptic problems via a monotonicity result which obtained by the method of moving planes with an improved Aleksandrov-Bakelman-Pucci (ABP) type estimate for the fractional Laplacian in unbounded domain.