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On a nonlinear elliptic system: resonance and bifurcation cases

Mario Zuluaga Uribe (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider an elliptic system at resonance and bifurcation type with zero Dirichlet condition. We use a Lyapunov-Schmidt approach and we will give applications to Biharmonic Equations.

On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces

Zuomao Yan (2011)

Annales Polonici Mathematici

This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.

On a problem of Gulevich on nonexpansive maps in uniformly convex Banach spaces

Sehie Park (1996)

Commentationes Mathematicae Universitatis Carolinae

Let X be a uniformly convex Banach space, D X , f : D X a nonexpansive map, and K a closed bounded subset such that co ¯ K D . If (1) f | K is weakly inward and K is star-shaped or (2) f | K satisfies the Leray-Schauder boundary condition, then f has a fixed point in co ¯ K . This is closely related to a problem of Gulevich [Gu]. Some of our main results are generalizations of theorems due to Kirk and Ray [KR] and others.

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