Search results for "Existence theorem"
showing 5 items of 15 documents
Existenzsätze für schwach nichtlineare Operatorgleichungen und Anwendung auf Randwertaufgaben mit gewöhnlichen Differentialgleichungen
1979
With Schauder's fixpoint principle we establish an existence theorem for solutions of two simultaneous nonlinear operator equations of the formL iu=Miu, i=1,2, Li linear,M i continous. By applying this result to boundary value problems with ordinary differential equations we generalize results of Conti and Ehrmann in various directions.
Best proximity points for cyclic Meir–Keeler contractions
2008
Abstract We introduce a notion of cyclic Meir–Keeler contractions and prove a theorem which assures the existence and uniqueness of a best proximity point for cyclic Meir–Keeler contractions. This theorem is a generalization of a recent result due to Eldred and Veeramani.
On the structure of the set of solutions of nonlinear equations
1971
Let T be a mapping from a subset of a Banach space X into a Banach space Y. The present paper investigates the nature of the set of solutions of the equation T(x) = y for a given y E Y, i.e. when T-l(y) # 0 ? What are the topological properties of T-l(y)? A prototype for an answer to these questions is given by Peano existence theorem on the connectedness of the set of solutions of an ordinary differential equation in the real case. In its general setting, this problem was first attacked by Aronszajn [l] and Stampacchia [l 11; recently, by Browder-Gupta [5], Vidossich [12] and, above all, Browder [3, Sec. 51 who gives several interesting results in an excellent treatment. Customary, the str…
SOME EXAMPLES RELATED TO A CLASS OF FUNCTIONALS WITHOUT GLOBAL MINIMA
2012
Abstract: In this paper, we provide six examples which show the sharpness of the assumptions of a recent deep result of Ricceri about a class of functionals without global minima.
Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces
2011
The purpose of this paper is to present some fixed point theorems for T -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations.