Some coincidence theorems in wedges, cones, and convex sets. (English) Zbl 0576.34018

Santanilla, Jairo

J. Math. Anal. Appl. 105, 357-371 (1985).

Coincidence degree is used to study the solvability of a semilinear equation in a prescribed convex set. Generalizations of the Schauder fixed point theorem and compression theorem by Krasnosel’skij are given. The author applies some of the abstract results to establish existence of nonnegative solutions to some boundary value problems involving ordinary differential equations.

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
47J05	Equations involving nonlinear operators (general)
47J25	Iterative procedures involving nonlinear operators

Keywords:

Coincidence degree; Schauder fixed point theorem; compression theorem

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