Abstract
In this paper, we study the quasilinear elliptic system with Sobolev critical exponent involving both concave-convex and Hardy terms in bounded domains. By employing the technique introduced by Benci and Cerami (1991), we obtain at least cat(Ω)+1 distinct positive solutions.
Highlights
Introduction and Main ResultIn this paper, we are concerned with the multiplicity of positive solutions of the following critical problem: −Δ pu − ] |u|p−2 |x|p u = 1 p∗∂F ∂u (x, u, V) + fλ (x) |u|q−2 u in Ω, −Δ pV |V|p−2 |x|p V
We are concerned with the multiplicity of positive solutions of the following critical problem:
Its proof is similar to the lemma [4]
Summary
We are concerned with the multiplicity of positive solutions of the following critical problem:. The function F satisfies the following conditions: (f1) F ∈ C1(Ω × (R+), R+), such that ∀t > 0. Many papers have studied the multiplicity of positive solutions by way of fibering method and the notions of topological indices category for different semilinear, quasilinear, and nonlocal problems involving a critical exponent and concave and convex nonlinearities (see [2,3,4]).
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