Sign-Changing Solutions of Fractional 𝑝-Laplacian Problems

Abstract

In this paper, we obtain the existence and multiplicity of sign-changing solutions of the fractional p-Laplacian problems by applying the method of invariant sets of descending flow and minimax theory. In addition, we prove that the problem admits at least one least energy sign-changing solution by combining the Nehari manifold method with the constrained variational method and Brouwer degree theory. Furthermore, the least energy of sign-changing solutions is shown to exceed twice that of the least energy solutions.

Keywords

• sign-changing solutions
• invariant sets
• descending flow
• nehari manifold
• 35j60
• 35j92
• 35r11
• 47j30