Dimension of the set of positive solutions to nonlinear equations and applications

Petronije S. Milojević

Dimension of the set of positive solutions to nonlinear equations and applications

Petronije S. Milojević

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We study the covering dimension of the set of (positive) solutions to various classes of nonlinear equations involving condensing and A-proper maps. It is based on the nontriviality of the fixed point index of a certain condensing map or on oddness of a nonlinear map. Applications to nonlinear singular integral equations and to semilinear ordinary and elliptic partial differential equations are given with finite or infinite dimensional null space of the linear part.

Original language	English (US)
Article number	213
Journal	Electronic Journal of Differential Equations
Volume	2016
State	Published - Aug 10 2016

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Condensing and A-proper maps
Covering dimension
Elliptic PDE’s
Exponential dichotomy
Fixed point index
Ordinary differential equations
Semilinear equations
Singular integral equations

Cite this

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abstract = "We study the covering dimension of the set of (positive) solutions to various classes of nonlinear equations involving condensing and A-proper maps. It is based on the nontriviality of the fixed point index of a certain condensing map or on oddness of a nonlinear map. Applications to nonlinear singular integral equations and to semilinear ordinary and elliptic partial differential equations are given with finite or infinite dimensional null space of the linear part.",

keywords = "Condensing and A-proper maps, Covering dimension, Elliptic PDE{\textquoteright}s, Exponential dichotomy, Fixed point index, Ordinary differential equations, Semilinear equations, Singular integral equations",

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note = "Publisher Copyright: {\textcopyright} 2016 Texas State University.",

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journal = "Electronic Journal of Differential Equations",

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AB - We study the covering dimension of the set of (positive) solutions to various classes of nonlinear equations involving condensing and A-proper maps. It is based on the nontriviality of the fixed point index of a certain condensing map or on oddness of a nonlinear map. Applications to nonlinear singular integral equations and to semilinear ordinary and elliptic partial differential equations are given with finite or infinite dimensional null space of the linear part.

KW - Condensing and A-proper maps

KW - Covering dimension

KW - Elliptic PDE’s

KW - Exponential dichotomy

KW - Fixed point index

KW - Ordinary differential equations

KW - Semilinear equations

KW - Singular integral equations

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VL - 2016

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

M1 - 213

ER -

Dimension of the set of positive solutions to nonlinear equations and applications

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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