Sign-changing solutions for the stationary Kirchhoff problems involving the fractional Laplacian in R^N

2017/01/14 by Kun Soo Chang, Qi Gao, Chang, Kun +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1701.03862

openalex publication_date 2017/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the existence of least energy sign-changing solutions for a Kirchhoff-type problem involving the fractional Laplacian operator. By using the constraint variational method and quantitative deformation lemma, we obtain a least energy nodal solution ub for the given problem. Moreover, we show that the energy of ub is strictly larger than twice the ground state energy. We also give a convergence property of u_b as b goes to 0, where b is regarded as a parameter.

Citations

• The Brezis-Nirenberg result for the fractional Laplacian
• Existence of solitary waves in higher dimensions

Related

• Signed and sign-changing solutions for a class Kirchhoff-type problem involving the fractional p-Laplacian with critical Hardy nonlinearity
• Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities
• The existence of least energy nodal solutions for some class of Kirchhoff equations and Choquard equations
• Existence of sign-changing solutions for a logarithmic weighted Kirchhoff problem in the whole of ℝ^N with exponential growth non-linearity
• Stationary Kirchhoff problems involving a fractional elliptic operator\n and a critical nonlinearity