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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 impulsive semilinear fractional differential inclusions with delay in Banach spaces

Hammouche Hadda, Guerbati Kaddour, Benchohra Mouffak, Abada Nadjat (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.

Existence results for nonlocal boundary value problems for fractional differential equations and inclusions with fractional integral boundary conditions

Sotiris K. Ntouyas (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with fractional integral boundary conditions. Some new existence results are obtained by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.

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