Loss of positivity in a nonlinear scalar heat equation

被引：90

作者：

Infante, Gennaro ^{[1
]}

Webb, J. R. L.

机构：

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

[2] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2006年 / 13卷 / 02期

关键词：

fixed point index; cone; positive solution;

D O I：

10.1007/s00030-005-0039-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the theory of fixed point index, we discuss the existence of nontrivial (multiple) solutions of a nonlinear scalar heat equation with nonlocal boundary conditions depending on a positive parameter. Solutions lose positivity as the parameter decreases. For a certain parameter range, not all solutions can be positive but there are positive solutions for certain types of nonlinearity. We also prove a uniqueness result.

引用

页码：249 / 261

页数：13

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