Non-trivial solutions of local and non-local Neumann boundary-value problems

被引：35

作者：

Infante, Gennaro ^{[1
]}

Pietramala, Paolamaria ^{[1
]}

Tojo, F. Adrian F. ^{[2
]}

机构：

[1] Univ Calabria, Dipartimento Matemat & Informat, I-87036 Cosenza, Italy

[2] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15782, Spain

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2016年 / 146卷 / 02期

关键词：

fixed-point index; cone; non-trivial solution; Neumann conditions; MULTIPLE POSITIVE SOLUTIONS; FIXED-POINT THEOREM; HAMMERSTEIN INTEGRAL-EQUATIONS; LINEAR-OPERATORS; DIFFERENTIAL-EQUATIONS; EXISTENCE; CONES;

D O I：

10.1017/S0308210515000499

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove new results on the existence, non-existence, localization and multiplicity of non-trivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed-point index. Some of the criteria involve a comparison with the spectral radius of some related linear operators. We apply our results to some boundary-value problems with local and non-local boundary conditions of Neumann type. We illustrate in some examples the methodologies used.

引用

页码：337 / 369

页数：33

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