NONLINEAR EQUATIONS INVOLVING THE SQUARE ROOT OF THE LAPLACIAN

被引：6
作者：
Ambrosio, Vincenzo [1 ]
Bisci, Giovanni Molica [2 ]
Repovs, Dusan [3 ,4 ]
机构：
[1] Univ Urbino Carlo Bo, Dipartimento Sci Pure & Applicate DiSPeA, Piazza Repubbl 13, I-61029 Urbino, Pesaro & Urbino, Italy
[2] Univ Mediterranea Reggio Calabria, Dipartimento PAU, I-89100 Reggio Di Calabria, Italy
[3] Univ Ljubljana, Fac Educ, SI-1000 Ljubljana, Slovenia
[4] Univ Ljubljana, Fac Math & Phys, SI-1000 Ljubljana, Slovenia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2019年 / 12卷 / 02期
关键词：
Fractional Laplacian; variational methods; multiple solutions; MULTIPLE SOLUTIONS; FRACTIONAL LAPLACIAN; EXISTENCE;
D O I：
10.3934/dcdss.2019011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we discuss the existence and non- existence of weak solutions to parametric fractional equations involving the square root of the Laplacian A(1/2) in a smooth bounded domain Omega subset of R-n (n >= 2) and with zero Dirichlet boundary conditions. Namely, our simple model is the following equation {A1/2u = lambda f(u) in Omega u = 0 on partial derivative Omega. The existence of at least two non-trivial L-infinity-bounded weak solutions is established for large value of the parameter A, requiring that the nonlinear term f is continuous, superlinear at zero and sublinear at infinity. Our approach is based on variational arguments and a suitable variant of the Caffarelli-Silvestre extension method.
引用
收藏
页码：151 / 170
页数：20
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