کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4615154 | 1339309 | 2015 | 21 صفحه PDF | دانلود رایگان |
The purpose of this paper is to investigate the existence of weak solutions for a Kirchhoff type problem driven by a non-local integro-differential operator of elliptic type with homogeneous Dirichlet boundary conditions as follows:{M(∫R2N|u(x)−u(y)|pK(x−y)dxdy)LKpu=f(x,u)inΩ,u=0inRN∖Ω, where LKp is a non-local operator with singular kernel K, Ω is an open bounded subset of RNRN with Lipshcitz boundary ∂Ω, M is a continuous function and f is a Carathéodory function satisfying the Ambrosetti–Rabinowitz type condition. We discuss the above-mentioned problem in two cases: when f satisfies sublinear growth condition, the existence of nontrivial weak solutions is obtained by applying the direct method in variational methods; when f satisfies suplinear growth condition, the existence of two nontrivial weak solutions is obtained by using the Mountain Pass Theorem.
Journal: Journal of Mathematical Analysis and Applications - Volume 424, Issue 2, 15 April 2015, Pages 1021–1041