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Periodic and Almost Periodic Solutions of Integral Inclusions

Radosław Pietkun (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

The existence of a continuous periodic and almost periodic solutions of the nonlinear integral inclusion is established by means of the generalized Schauder fixed point theorem.

Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces

Dimitrios A. Kandilakis, Nikolaos S. Papageorgiou (1997)

Commentationes Mathematicae Universitatis Carolinae

In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we impose a compactness condition using the ball measure of noncompactness. We obtain the extremal solutions...

Perturbed Hammerstein integral inclusions with solutions that change sign

Gennaro Infante, Paolamaria Pietramala (2009)

Commentationes Mathematicae Universitatis Carolinae

We establish new existence results for nontrivial solutions of some integral inclusions of Hammerstein type, that are perturbed with an affine functional. In order to use a theory of fixed point index for multivalued mappings, we work in a cone of continuous functions that are positive on a suitable subinterval of [ 0 , 1 ] . We also discuss the optimality of some constants that occur in our theory. We improve, complement and extend previous results in the literature.

Positive solutions for a system of fractional boundary value problems

Henderson, Johnny, Luca, Rodica (2017)

Proceedings of Equadiff 14

We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with nonnegative nonlinearities which can be nonsingular or singular functions, subject to multi-point boundary conditions that contain fractional derivatives.

Positive solutions of a renewal equation

Janusz Traple (1992)

Annales Polonici Mathematici

An existence theorem is proved for the scalar convolution type integral equation x ( t ) = - h ( t - s ) f ( s , x ( s ) ) d s .

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