Positive, negative and least energy nodal solutions for Kirchhoff equations in ℝN.

The paper deals with the following Kirchhoff equations: − a + b ∫ R N | ∇ u | 2 d x △ u + V (x) u = K (x) f (u) i n R N , u ∈ H 1 (R N) , where N ≥ 3 , f (u) is C 1 real function satisfying quasicritical growth at infinity, and V (x) , K (x) 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 u 0 with two nodal domains. Finally, we show that the energy of u 0 is strictly larger than the ground state energy. [ABSTRACT FROM AUTHOR]