The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions

Abstract

This paper examines a class of Kirchhoff type equations that involve sign-changing weight functions. Using Nehari manifold and fibering map, the existence of multiple positive solutions is established.

The Choquard Equation with Weighted Terms and Sobolev-Hardy Exponent

“…Furthermore, by means of the tool of Nehari manifold, Zhang et al [36] established the existence theorem of ground states for generalized Choquard equation when the nonlinear term is concave-convex. On the other hand, there are a great deal of results on the existence of elliptic boundary value problems with sign-changing weights [37][38][39][40][41][42][43][44][45]. We should point out that Hsu and Lin [38] showed the existence of positive solutions for elliptic equations with concave-convex nonlinearities and sign-changing weights.…”

“…In view of the same method, Chen and Wu [41] obtained the existence of positive solutions for a class of critical semilinear problem. Chen et al [42] established multiplicity .…”

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. As for in nitely many solutions, we refer readers to [8] [9].…”

MULTIPLE SOLUTIONS FOR A p-LAPLACIAN SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

“…The main approach of this paper is the method of Nehari manifold, which was first introduced by Nehari in [31,32], and the method turned out to be very useful in critical point theory (see, e.g., [1,2,10,11,14,15,25,37,38,40,41]) and eventually came to bear his name.…”