Existence results of positive solutions of Kirchhoff type problems

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:…”

Infinitely many large energy solutions for Schrödinger-Kirchhoff type problem in RN

“…It was pointed out in [9] that Kirchhoff type problem (1.3) models several physical and biological systems, where u describes a process which depends on the average of itself (for example, population density). Moreover, a lot of interesting studies by variational methods can be found in [2,6,7,8,10,15,16,18,20,27] for Kirchhoff type problem (1.3) on bounded domain with several growth conditions on g.…”

Existence and Concentration Results for Kirchhoff-Type Schrö Dinger Systems With Steep Potential Well

“…He and Zou [7] showed existence of infinitely many solutions by using the local minimum methods and the fountain theorems. Cheng and Wu [5] studied the existence of positive solutions for problem (1.1) when the nonlinearity f is asymptotically t 3 -growth at infinity. We also note that problem (1.1) is related to the stationary analogue of the equation…”