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

页码：151 / 170

页数：20

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