Strongly nonlinear nonhomogeneous elliptic unilateral problems with L 1 data and no sign conditions (original) (raw)

Existence of solutions for some nonlinear elliptic unilateral problems with measure data

Electronic Journal of Qualitative Theory of Differential Equations, 2013

In this paper, we prove the existence of an entropy solution to unilateral problems associated to the equations of the type: Au + H(x, u, ∇u) − divφ(u) = µ ∈ L 1 (Ω) + W −1,p (x) (Ω), where A is a Leray-Lions operator acting from W 1,p(x) 0 (Ω) into its dual W −1,p(x) (Ω), the nonlinear term H(x, s, ξ) satisfies some growth and the sign conditions and φ(u) ∈ C 0 (R, R N).

Existence of solutions for some nonlinear elliptic unilateral problems having L 1 data

Lobachevskii Journal of Mathematics, 2011

In this paper, we study the existence of solutions to the following nonlinear elliptic problem in a bounded subset Ω of R N : −∆pu = f (x, u, ∇u) + µ in Ω, u = 0 on ∂Ω, where µ is a Radon measure on Ω which is zero on sets of p-capacity zero, f : Ω×R×R N → R is a Carathéodory function that satisfies certain conditions with respect to the one dimensional spectrum.

Strongly nonlinear degenerated unilateral problems with L^1 data

In this paper, we study the existence of solutions for strongly nonlinear degenerated unilateral problems associated to nonlinear operators of the form Au+g(x,u,ablau)Au+g(x,u,abla u)Au+g(x,u,ablau). Here AAA is a Leray-Lions operator acting from W01,p(Omega,w)W_0^{1,p}(Omega,w)W01,p(Omega,w) into its dual, while g(x,s,xi)g(x,s,xi)g(x,s,xi) is a nonlinear term which has a growth condition with respect to xixixi and no growth condition with respect to sss, the second term belongs to L1(Omega)L^{1}(Omega )L1(Omega).

Strongly nonlinear elliptic variational unilateral problems in Orlicz space

Abstract and Applied Analysis, 2006

We will be concerned with the existence result of unilateral problem associated to the equations of the formAu+g(x,u,∇u)=f, whereAis a Leray-Lions operator from its domainD(A)⊂W01LM(Ω)intoW−1EM¯(Ω). On the nonlinear lower order termg(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to|∇u|, and satisfies the sign condition. The right-hand sidefbelongs toW−1EM¯(Ω).

Solutions of nonlinear elliptic problems with lower order terms

Annals of Functional Analysis, 2015

We give an existence result for strongly nonlinear elliptic equations of the form −div(a(x, u, ∇u)) + g(x, u, ∇u) + H(x, ∇u) = µ in Ω, where the right hand side belongs to L 1 (Ω) + W −1,p (Ω) and −div(a(x, u, ∇u)) is a Leray-Lions type operator with growth |∇u| p−1 in ∇u. The critical growth condition on g is with respect to ∇u and no growth condition with respect to u, while the function H(x, ∇u) grows as |∇u| p−1 .