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

Abstract

In this paper, we show the existence and multiplicity of solutions for the following fourthorder Kirchhoff type elliptic equationsis of sublinear growth and h(x, u) satisfies some general 3-superlinear growth conditions at infinity. We show the existence of at least one solution for above equations for λ = 0. For λ > 0 small enough, we obtain at least two nontrivial solutions. Furthermore, if f (x, u) is odd in u, we show that above equations possess infinitely many solutions for all λ ≥ 0. Our theorems generalize some known results in the literatures even for λ = 0 and our proof is based on the variational methods.

Multiple solutions for superlinear Klein–Gordon–Maxwell equations†

“…This case has also been studied in many papers (see [4, 10, 12, 16–19]). Many authors (see [12, 18, 25, 27]) considered the following coercive condition.…”

Multiple solutions for superlinear Klein-Gordon-Maxwell equations

“…This case has also been studied in many papers(see [5,9,12,15,[17][18][19]). Many authors(see [12,18,22,23]) considered the following coercive condition.…”

Existence results of positive solutions for Kirchhoff type biharmonic equationvia bifurcation methods

“…In one-dimensional case ( N = 1 ), by using variational methods and some fixed point theorems in cones, the existence and multiplicity results for (1.1) with other boundary conditions are considered in [22][23][24][25]. In multidimensional case, also by using the variational methods, [12,13,31] studied the existence and multiplicity of nontrivial solutions for (1.1); and for similar problems in the whole space R N , see [3,7,11,26,29,[33][34][35] and the reference therein.…”