MULTIPLICITY RESULTS FOR NONLOCAL FRACTIONAL p-KIRCHHOFF EQUATIONS VIA MORSE THEORY

作者：Zhang Binlin^*; Bisci, Giovanni Molica; Xiang, Mingqi

来源：Topological Methods in Nonlinear Analysis, 2017, 49(2): 445-461.

DOI：10.12775/TMNA.2016.081

• Fractional p-Laplacian
• Kirchhoff type equations
• Morse theory
• local linking

In this paper, we apply Morse theory and local linking to study the existence of nontrivial solutions for Kirchhoff type equations involving the nonlocal fractional p-Laplacian with homogeneous Dirichlet boundary conditions: @@@ {[M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(p) /vertical bar x - y vertical bar(N+ps) dx dy)](p-1) (-Delta)(p)(s)u(x) = f(x, u) in Omega, u = 0 in R-N \ Omega, @@@ where Omega is a smooth bounded domain of R-N, (-Delta)(p)(s) is the fractional p-Laplace operator with 0 < s < 1 < p < infinity with sp < N, M: R-0(+) -> R+ is a continuous and positive function not necessarily satisfying the increasing condition and f is a Caratheodory function satisfying some extra assumptions.

• 出版日期2017-6
• 单位中国民航大学; 黑龙江工程学院