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Existence Principles for Singular Vector Nonlocal Boundary Value Problems with φ -Laplacian and their Applications

Staněk, Svatoslav (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Existence principles for solutions of singular differential systems ( φ ( u ' ) ) ' = f ( t , u , u ' ) satisfying nonlocal boundary conditions are stated. Here φ is a homeomorphism N onto N and the Carathéodory function f may have singularities in its space variables. Applications of the existence principles are given.

Existence results for boundary value problems for fourth-order differential inclusions with nonconvex valued right hand side

A. Arara, Mouffak Benchohra, Sotiris K. Ntouyas, Abdelghani Ouahab (2004)

Archivum Mathematicum

In this paper a fixed point theorem due to Covitz and Nadler for contraction multivalued maps, and the Schaefer’s theorem combined with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued operators with decomposables values, are used to investigate the existence of solutions for boundary value problems of fourth-order differential inclusions.

Existence results for delay second order differential inclusions

Dalila Azzam-Laouir, Tahar Haddad (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.

Existence results for systems with nonlinear coupled nonlocal initial conditions

Octavia Bolojan, Gennaro Infante, Radu Precup (2015)

Mathematica Bohemica

The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples are...

Existence theorem for the Hammerstein integral equation

Mieczysław Cichoń, Ireneusz Kubiaczyk (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we prove an existence theorem for the Hammerstein integral equation x ( t ) = p ( t ) + λ I K ( t , s ) f ( s , x ( s ) ) d s , where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.

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