Electron. J. Diff. Equ., Vol. 2016 (2016), No. 213, pp. 1-33.

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

Petronije S. Milojevic

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.

Submitted May 7, 2016. Published August 10, 2016.
Math Subject Classifications: 47H08, 47H09, 47J05, 45G05, 35L61.
Key Words: Covering dimension, semilinear equations; fixed point index; condensing and A-proper maps; singular integral equations; exponential dichotomy; ordinary differential equations; elliptic PDE's.

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Petronije S. Milojevic
Department of Mathematical Sciences and CAMS
New Jersey Institute of Technology
Newark, NJ 07102, USA
email: petronije.milojevic@njit.edu

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