Positive solutions for a quasilinear elliptic equation of Kirchhoff type

Multiple solutions for a class of Kirchhoff type problems with concave nonlinearity

“…Alves [1], Ma-Rivera [14] and HeZou [11] studied the existence of positive solutions and infinitely many positive solutions of the problem (1.3) by variational methods, respectively; Perera and Zhang [17] obtained one nontrivial solutions of (1.3) by Yang index theory; Mao-Zhang [15], Zhang and Perera [20] got three nontrivial solutions (a positive solution, a negative solution, a sign changing solution) of (1.3) by invariant sets of descent flow; Cheng-Wu [6] obtained the existence results of positive solutions of problem (1.3), also in [7] they used a three critical point theorem due to Brezis-Nirenberg [4] and a Z 2 version of the Mountain Pass Theorem due to Rabinowitz [19] to study the existence of multiple nontrivial solutions of problem (1.3) under some weaker assumptions. In order to establish multiple solutions for problem (1.1), we make the following assumptions:…”

Four Nontrivial Solutions for Kirchhoff Problems with Critical Potential, Critical Exponent and a Concave Term

“…For instance, positive solutions could be obtained in [2]- [4]. Especially, Chen et al [5] [6], Mao and Luan [7], found sign-changing solutions.…”

Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problems

“…can be used for modeling several physical and biological systems where u describes a process which depends on the average of it self, such as the population density, see [3]. The study of Kirchhoff type equations has already been extended to the case involving the p-Laplacian…”