Abstract
In this paper, we use the Fountain Theorem and the Dual Fountain Theorem to study the existence of infinitely many solutions for Kirchhoff type equations involving nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian of Kirchhoff type:{M(∬R2N|u(x)−u(y)|2|x−y|N+2sdxdy)(−Δ)su(x)−λu=f(x,u)in Ωu=0in RN∖Ω, where Ω is a smooth bounded domain of RN, (−Δ)s is the fractional Laplacian operator with 0<s<1 and 2s<N, λ is a real parameter, M is a continuous and positive function and f is a Carathéodory function satisfying the Ambrosetti–Rabinowitz type condition.
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