Jorge Villanueva Cossio - Academia.edu (original) (raw)
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Papers by Jorge Villanueva Cossio
Progress in Nonlinear Differential Equations and Their Applications, 2006
ABSTRACT We provide a method for finding a radial solution to a superlinear Dirichlet problem in ... more ABSTRACT We provide a method for finding a radial solution to a superlinear Dirichlet problem in a ball that changes sign exactly once and implement it using mathematical software. As a by-product, we conclude that the least energy sign changing solution for that problem is nonradial, which has been proved using different methods by A. Aftalion, Amandine, F. Pacella [C. R., Math., Acad. Sci. Paris 339, No. 5, 339–344 (2004; Zbl 1113.35063)], T. Bartsch, T. Weth and M. Willem [J. Anal. Math. 96, 1–18 (2005; Zbl 1206.35086)].
Rocky Mountain Journal of Mathematics, 1997
We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair... more We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].
Annali di Matematica Pura ed Applicata, 2011
ABSTRACT In this paper, we establish sufficient conditions for an asymptotically linear elliptic ... more ABSTRACT In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov–Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.
SIAM Journal on Mathematical Analysis, 1994
Nonlinear Analysis: Theory, Methods & Applications, 2009
In this paper we prove that an asymptotically linear Dirichlet problem has at least three nontriv... more In this paper we prove that an asymptotically linear Dirichlet problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first k eigenvalues of minus Laplacian, without any restriction about nondegeneracy of solutions. A pair is of one sign (positive and negative, respectively). We construct a third solution using arguments of the type Lazer-Solimini (see [A.C. Lazer, S. Solimini, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonlinear Anal. 12 (8) (1988) 761-775]). This gives a partial answer to a conjecture stated in [J. Cossio, S. Herrón, Nontrivial solutions for a semilinear Dirichlet problem with nonlinearity crossing multiple eigenvalues, J. Dyn. Differential Equations 16 (3) (2004) 795-803]. Moreover, in the particular case of nondegenerate critical points, we prove that there are at least four nontrivial solutions, the one sign solutions are of Morse index equal to 1, the third solution has Morse index k, and there is a fourth solution. For this case, we use the Leray-Schauder degree and Lazer-Solimini results.
Nonlinear Analysis: Theory, Methods & Applications, 1997
Nonlinear Analysis: Theory, Methods & Applications, 2001
Journal of Mathematical Analysis and Applications, 2008
Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichle... more Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichlet problem in annulii. Our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions. We prove that, for k > 0 large, there exist exactly two radial solutions with k nodal regions (connected components of {x: u(x) = 0}). The problem need not be homogeneous.
Journal of Mathematical Analysis and Applications, 2008
We prove that an asymptotically linear Dirichlet problem which involves the p-Laplacian operator ... more We prove that an asymptotically linear Dirichlet problem which involves the p-Laplacian operator has multiple radial solutions when the nonlinearity has a positive zero and the range of the 'p-derivative' of the nonlinearity includes at least the first j radial eigenvalues of the p-Laplacian operator. The main tools that we use are a uniqueness result for the p-Laplacian operator and bifurcation theory.
Journal of Mathematical Analysis and Applications, 2013
Journal of Mathematical Analysis and Applications, 2011
We prove the existence of infinitely many radial solutions for a p-Laplacian Dirichlet problem wh... more We prove the existence of infinitely many radial solutions for a p-Laplacian Dirichlet problem which is p-superlinear at the origin. The main tool that we use is the shooting method. We extend for more general nonlinearities the results of J. Iaia in [J. Iaia, Radial solutions to a p-Laplacian Dirichlet problem, Appl. Anal. 58 (1995) 335-350]. Previous developments require a behavior of the nonlinearity at zero and infinity, while our main result only needs a condition of the nonlinearity at zero.
Journal of Dynamics and Differential Equations, 2004
ABSTRACT In this paper we prove that a semilinear elliptic boundary value problem has at least th... more ABSTRACT In this paper we prove that a semilinear elliptic boundary value problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues of the Laplacian and all solutions are nondegenerate. A pair are of one sign (positive and negative, respectively). The one sign solutions are of Morse index less than or equal to 1 and the third solution has Morse index greater than or equal to 2. Extensive use is made of the mountain pass theorem, and Morse index arguments of the type Lazer–Solimini (see Lazer and Solimini, Nonlinear Anal. 12(8), 761–775, 1988). Our result extends and complements a theorem of Cossio and Veléz, Rev. Colombiana Mat. 37(1), 25–36, 2003.
Discrete and Continuous Dynamical Systems, 2012
Somos un empresa que se especializa en el montaje y mantenimiento electromecánico de líneas y sub... more Somos un empresa que se especializa en el montaje y mantenimiento electromecánico de líneas y subestaciones de alta, media y baja tensión.
Progress in Nonlinear Differential Equations and Their Applications, 2006
ABSTRACT We provide a method for finding a radial solution to a superlinear Dirichlet problem in ... more ABSTRACT We provide a method for finding a radial solution to a superlinear Dirichlet problem in a ball that changes sign exactly once and implement it using mathematical software. As a by-product, we conclude that the least energy sign changing solution for that problem is nonradial, which has been proved using different methods by A. Aftalion, Amandine, F. Pacella [C. R., Math., Acad. Sci. Paris 339, No. 5, 339–344 (2004; Zbl 1113.35063)], T. Bartsch, T. Weth and M. Willem [J. Anal. Math. 96, 1–18 (2005; Zbl 1206.35086)].
Rocky Mountain Journal of Mathematics, 1997
We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair... more We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12].
Annali di Matematica Pura ed Applicata, 2011
ABSTRACT In this paper, we establish sufficient conditions for an asymptotically linear elliptic ... more ABSTRACT In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov–Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.
SIAM Journal on Mathematical Analysis, 1994
Nonlinear Analysis: Theory, Methods & Applications, 2009
In this paper we prove that an asymptotically linear Dirichlet problem has at least three nontriv... more In this paper we prove that an asymptotically linear Dirichlet problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first k eigenvalues of minus Laplacian, without any restriction about nondegeneracy of solutions. A pair is of one sign (positive and negative, respectively). We construct a third solution using arguments of the type Lazer-Solimini (see [A.C. Lazer, S. Solimini, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonlinear Anal. 12 (8) (1988) 761-775]). This gives a partial answer to a conjecture stated in [J. Cossio, S. Herrón, Nontrivial solutions for a semilinear Dirichlet problem with nonlinearity crossing multiple eigenvalues, J. Dyn. Differential Equations 16 (3) (2004) 795-803]. Moreover, in the particular case of nondegenerate critical points, we prove that there are at least four nontrivial solutions, the one sign solutions are of Morse index equal to 1, the third solution has Morse index k, and there is a fourth solution. For this case, we use the Leray-Schauder degree and Lazer-Solimini results.
Nonlinear Analysis: Theory, Methods & Applications, 1997
Nonlinear Analysis: Theory, Methods & Applications, 2001
Journal of Mathematical Analysis and Applications, 2008
Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichle... more Here we establish the existence of infinitely many nonradial solutions for a superlinear Dirichlet problem in annulii. Our proof relies on estimating the number of radial solutions having a prescribed number of nodal regions. We prove that, for k > 0 large, there exist exactly two radial solutions with k nodal regions (connected components of {x: u(x) = 0}). The problem need not be homogeneous.
Journal of Mathematical Analysis and Applications, 2008
We prove that an asymptotically linear Dirichlet problem which involves the p-Laplacian operator ... more We prove that an asymptotically linear Dirichlet problem which involves the p-Laplacian operator has multiple radial solutions when the nonlinearity has a positive zero and the range of the 'p-derivative' of the nonlinearity includes at least the first j radial eigenvalues of the p-Laplacian operator. The main tools that we use are a uniqueness result for the p-Laplacian operator and bifurcation theory.
Journal of Mathematical Analysis and Applications, 2013
Journal of Mathematical Analysis and Applications, 2011
We prove the existence of infinitely many radial solutions for a p-Laplacian Dirichlet problem wh... more We prove the existence of infinitely many radial solutions for a p-Laplacian Dirichlet problem which is p-superlinear at the origin. The main tool that we use is the shooting method. We extend for more general nonlinearities the results of J. Iaia in [J. Iaia, Radial solutions to a p-Laplacian Dirichlet problem, Appl. Anal. 58 (1995) 335-350]. Previous developments require a behavior of the nonlinearity at zero and infinity, while our main result only needs a condition of the nonlinearity at zero.
Journal of Dynamics and Differential Equations, 2004
ABSTRACT In this paper we prove that a semilinear elliptic boundary value problem has at least th... more ABSTRACT In this paper we prove that a semilinear elliptic boundary value problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues of the Laplacian and all solutions are nondegenerate. A pair are of one sign (positive and negative, respectively). The one sign solutions are of Morse index less than or equal to 1 and the third solution has Morse index greater than or equal to 2. Extensive use is made of the mountain pass theorem, and Morse index arguments of the type Lazer–Solimini (see Lazer and Solimini, Nonlinear Anal. 12(8), 761–775, 1988). Our result extends and complements a theorem of Cossio and Veléz, Rev. Colombiana Mat. 37(1), 25–36, 2003.
Discrete and Continuous Dynamical Systems, 2012
Somos un empresa que se especializa en el montaje y mantenimiento electromecánico de líneas y sub... more Somos un empresa que se especializa en el montaje y mantenimiento electromecánico de líneas y subestaciones de alta, media y baja tensión.