Existence of solutions for perturbed elliptic system with critical exponents

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 multiplicity of positive solutions for a coupled system of perturbed nonlinear fractional differential equations

In this paper, we consider a coupled system of nonlinear fractional differential equations (FDEs), such that both equations have a particular perturbed terms. Using emph{Leray-Schauder} fixed point theorem, we investigate the existence and multiplicity of positive solutions for this system.

Existence result for semilinear elliptic systems involving critical exponents

where ⊂RN (N ≥ ) is a smooth bounded domain such that ξi ∈ , i = , , . . . ,k, k ≥ , are different points, ≤ μi < μ̄ := (N–  ), L := – · – ∑k i=μi · |x–ξi| , η,λ,σ ≥ , a,a,a ∈ R,  < α, β < ∗ – , α + β = ∗. We work in the product space H ×H , where the space H :=H ( ) is the completion of C∞  ( ) with respect to the norm ( ∫ |∇ · | dx)   . In resent years many publications...

Nodal Solutions of Elliptic Equations with Critical Sobolev Exponents

Existence of solutions for elliptic systems with critical Sobolev exponent ∗

We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.