Sign-changing solutions for Kirchhoff-type variable-order fractional Laplacian problems

Abstract

Abstract In this paper, we are concerned with the Kirchhoff-type variable-order fractional Laplacian problems involving critical exponents and logarithmic nonlinearity. By using the constraint variational method, we show the existence of one least energy sign-changing solution. Moreover, we show that this energy is strictly larger than twice the ground energy.

Keywords

• Kirchhoff-type problem
• Variable-order fractional Laplacian
• Sign-changing solution