Solutions for fourth-order Kirchhoff type elliptic equations involving concave–convex nonlinearities in RN

Multiple Positive Solutions for Semilinear Elliptic Equations in RN Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions

and Applied Analysis 3 Theorem 1.1. Assume that (A1) and (B1) hold. If λ ∈ 0,Λ0 , then Eλa,b admits at least one positive solution inH1 R . Associated with Eλa,b , we consider the energy functional Jλa,b inH1 R : Jλa,b u 1 2 ‖u‖H1 − λ q ∫ RN a x |u|dx − 1 p ∫

Multiple Positive Solutions for Kirchhoff Type Problems Involving Concave and Convex Nonlinearities in R

In this article, we consider the multiplicity of positive solutions for a class of Kirchhoff type problems with concave and convex nonlinearities. Under appropriate assumptions, we prove that the problem has at least two positive solutions, moreover, one of which is a positive ground state solution. Our approach is mainly based on the Nehari manifold, Ekeland variational principle and the theor...

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Multiple Solutions of Quasilinear Elliptic Equations in RN

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems