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Existence of mild solutions on infinite intervals to first order initial value problems for a class of differential inclusions in banach spaces

Mouffak Benchohra (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we investigate the existence of mild solutions on an unbounded real interval to first order initial value problems for a class of differential inclusions in Banach spaces. We shall make use of a theorem of Ma, which is an extension to multivalued maps on locally convex topological spaces of Schaefer's theorem.

Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems

Evgenia H. Papageorgiou, Nikolaos S. Papageorgiou (2004)

Czechoslovak Mathematical Journal

In this paper we examine nonlinear periodic systems driven by the vectorial p -Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e. p = 2 ) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem...

Existence of solutions for fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions

Bashir Ahmad, Sotiris Ntouyas (2014)

Mathematica Bohemica

In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the multivalued map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative...

Existence of solutions for hyperbolic differential inclusions in Banach spaces

Nikolaos S. Papageorgiou (1992)

Archivum Mathematicum

In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of noncompactness we prove two existence theorems. The first for problems with convex valued orientor fields and the second for problems with nonconvex valued ones.

Existence of solutions for integrodifferential inclusions in Banach spaces

Nikolaos S. Papageorgiou (1991)

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.

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