Positive, negative and least energy nodal solutions for Kirchhoff equations in ℝ N

Abstract

The paper deals with the following Kirchhoff equations: where , is real function satisfying quasicritical growth at infinity, and are positive and continuous functions. Combining Mountain Pass Theorem and compact embeddings in weighted Sobolev spaces, we establish the existence of at least a positive and a negative solution. Moreover, using a quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution with two nodal domains. Finally, we show that the energy of is strictly larger than the ground state energy.