Infinitely many sign-changing solutions for modified Kirchhoff-type equations in ℝ3

Abstract

ABSTRACT Consider a class of modified Kirchhoff-type equations where the nonlinear term f is 4-superlinear at infinity. By using the method of invariant sets of descending flow, the existence of a sign-changing solution is obtained. When f is assumed to be odd, we prove that the above problem admits infinitely many sign-changing solutions. Moreover, when and the nonlinearity of power growth with 1<p, we establish some existence and non-existence results. For , the non-existence result relies on the deduction of some suitable Pohozaev identity. For , using the Nehari–Pohozaev manifold, we prove that the above problem admits a ground state solution.