On a class of nonlocal elliptic problems with critical growth

Abstract

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff typewhere Ω ⊂ R N , for N=1,2 and 3, is a bounded smooth domain, M and f are continuous functions and λ is a positive parameter. Our approach is based on the variational method.Mathematics subject classification (2010): 34B18, 34C11, 34K12, 35J25, 45M20.

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

“…There are some recent papers on the Kirchhoff type of problem involving critical exponent, see [21,1,7,11,8]. In particular, in [1], Alves, Corrêa, and Figueiredo have studied the existence of solutions for equations…”

Existência E Multiplicidade De Soluções Para Uma Equação Elítica Quaselinear Do Tipo Kirchhoff

“…Citamos ainda dentre outros, os trabalhos de Alves et al (2005), Dai (2009), Dai e Liu (2009), Dai e Wei (2010), Alves et al (2010), Miotto (2010), Cammaroto e Vilasi (2011), Colasuonno e Pucci (2011), Sun e Tang (2011), Pei (2012, Huang et al (2013), Hssini et al (2013), Ferrara et al (2014, Miotto (2014) e Hssini et al (2015 os quais utilizam argumentos variacionais.…”

Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent

“…Recall that S is attained by the function (3.19) and (3,6), (3.20) where K 1 , K 2 are positive constants. Moreover,…”

“…Perera and Zhang [40] obtained nontrivial solutions for (1.1) with the aid of the Yang index and critical groups. When f (x, u) is a continuous superlinear nonlinearity with critical growth, Alves et al [3] proved the existence of positive solution for (1.1). In Zhang and Perera [46] and Mao and Zhang [38], the authors used minimax methods and invariant sets of descent flow to prove the existence of three solutions (a positive solution, a negative solution and a sign-changing solution) for (1.1).…”