Multiple solutions for Kirchhoff-type equations in $\mathbb {R}^N$RN

Abstract

Articles you may be interested inTemperature dependence of electronic behaviors in n-type multiple-channel junctionless transistors A fourth-order adaptive collocation approach for the solution of generalized Emden-Fowler type equations AIP Conf.This paper is devoted to the existence of infinitely many solutions for a class of Kirchhoff-type equations setting on R N . Based on the minimax methods in critical point theory, we obtain infinitely many large-energy and small-energy solutions, which unify and sharply improve the recent results of Wu ["Existence of nontrivial solutions and high energy solutions for Schrödinger-Kirchhoff-type equations in

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

“…In recent years, a lot of scholars have studied the singular Kirchhoff problem (for more details, we refer the reader to [1][2][3][4]), the Schrödinger-Poisson system (we refer the reader to [5][6][7][8]), and the Kirchhoff-Schrödinger-Poisson system (we refer the reader to [9][10][11][12]). The authors use various methods to obtain the properties of the solution, which makes such problems very interesting.…”

Multiple positive solutions for a class of Kirchhoff type equations in R N $\mathbb{R}^{N}$

“…where a, b are positive constants, N = 1, 2, 3, has been widely investigated by many authors, for example [1][2][3][4][5][6], etc. But in those papers, the nonlinearity f satisfies 3-superlinear growth at infinity, which assures the boundedness of any Palais-Smale sequence or Cerami sequence.…”

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

“…Many solvability conditions on the nonlinearity have been given to obtain the existence and multiplicity of solutions for Kirchhoff type problems in R N , we refer the readers to [3,4,11,12,14,17,23,24,25,26] and references therein. Particularly, Wu obtained four results of the existence of a sequence of high energy solutions for the problem (1.1) by means of symmetric mountain pass theorem in [25].…”

“…Particularly, Wu obtained four results of the existence of a sequence of high energy solutions for the problem (1.1) by means of symmetric mountain pass theorem in [25]. Those results had been subsequently unified and improved by Y. Ye and C. Tang with the aid of fountain theorem in [26].…”

“…(ii) From Remark 1 in [26], the condition (g 1 ) is much weaker than the combination of usual subcritical condition and asymptotically linear condition near zero. Furthermore, condition (g 3 ) is much weaker than the following condition:…”