Infinitely many solutions for a nonlocal elliptic system of $(p_1,\ldots,p_n)$-Kirchhoff type with critical exponent

Existence of Infinitely Many Solutions for Perturbed Kirchhoff Type Elliptic Problems with Hardy Potential

In this article, by using critical point theory, we show the existence of infinitely many weak solutions for a fourth-order Kirchhoff type elliptic problems with Hardy potential.

Infinitely Many Solutions for a Fourth–order Nonlinear Elliptic System

In this paper we study the existence of solutions for the nonlinear elliptic system ⎪⎪⎨ ⎪⎪⎩ Δu−Δu+V1(x)u = fu(x,u,v), Δv−Δv+V2(x)v = fv(x,u,v), u,v ∈ H(R) x ∈ R , where V1(x) and V2(x) are positive continue functions. Under some assumptions on fu(x,u,v) and fv(x,u,v) , we prove the existence of many nontrivial high and small energy solutions by variant Fountain theorems. This generalizes the re...

Solutions of an Elliptic System with a Nearly Critical Exponent

This problem has positive solutions for ǫ > 0 (with pqǫ > 1) and no non-trivial solution for ǫ ≤ 0. We study the asymptotic behaviour of least energy solutions as ǫ → 0. These solutions are shown to blow-up at exactly one point, and the location of this point is characterized. In addition, the shape and exact rates for blowing up are given. Résumé. Considéré le problème −∆uǫ = v p ǫ vǫ > 0 en Ω...

Infinitely Many Entire Solutions of an Elliptic System with Symmetry

On nonlocal elliptic system of $p$-Kirchhoff-type in $mathbb{R}^N$

‎Using Nehari manifold methods and Mountain pass theorem‎, ‎the existence of nontrivial and radially symmetric solutions for a class of $p$-Kirchhoff-type system are established.