Expansion-compression fixed point theorem of Leggett-Williams type for the sum of two operators and applications for some classes of BVPs

Author:

Benslimane Salim, ,Georgiev Svetlin G.,Mebarki Karima, ,

Abstract

"The purpose of this work is to establish an extension of a Leggett- Williams type expansion-compression fixed point theorem for a sum of two operators. As illustration, our approach is applied to prove the existence of non trivial nonnegative solutions for two-point BVPs and three-point BVPs."

Publisher

Babes-Bolyai University

Subject

General Mathematics

Reference20 articles.

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2. 2. Anderson, D.R., Avery, R.I., Henderson, J., Functional expansion-compression fixed point theorem of Leggett-Williams type, Electron. J. Differential Equations, 63(2010), 1-9.

3. 3. Avery, R.I., Henderson, J., Anderson, D.R., A topological proof and extension of the Leggett-Williams fixed point theorem, Applied Nonlinear Analysis. Dokl. 16(2009), no.4, 39-44.

4. 4. Avery, R.I., Henderson, J., O'Regan, D., Dual of the compression-expansion fixed point theorems, Fixed Point Theory Appl., 2007(2007), Article ID 90715, 11 pages.

5. 5. Banas, J., Goebel, K., Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure and Applied Mathematics, 60 Marcel Dekker, Inc., New York, 1980.

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