Existence and nonexistence of solutions for elliptic problems with multiple critical exponents

ON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS

In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Existence and Nonexistence of Positive Singular Solutions for Semilinear Elliptic Problems with Applications in Astrophysics

Existence of Positive Solutions for Quasilinear Elliptic Systems with Sobolev Critical Exponents

In this paper, we consider the existence of positive solutions to the following problem ⎪⎪⎨ ⎪⎪⎩ −div(|∇u|p−2∇u) = ∂F ∂u (u,v)+ ε p−1g(x) in Ω, −div(|∇v|q−2∇v) = ∂F ∂v (u,v)+ εq−1h(x) in Ω, u,v > 0 in Ω, u = v = 0 on ∂Ω, where Ω is a bounded smooth domain in RN ; F ∈C1((R+)2,R+) is positively homogeneous of degree μ ; g,h ∈C1(Ω)\{0} ; and ε is a positive parameter. Using sub-supersolution method...

Existence and Nonexistence of Positive Solutions for Singular Semilinear Elliptic Boundary Value Problems

In this paper we study existence of positive solutions to singular elliptic boundary value problems involving divergence terms in general domains. By constructing suitable upper and lower solutions and making comparison, we obtain suucient conditions for existence and nonexistence of solutions. We also study a concrete example to show that the conditions imposed on parameters appearing in the s...