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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.

Existence results for a class of quasilinear integrodifferential equations of Volterra-Hammerstein type with nonlinear boundary conditions

Zuodong Yang (2004)

Annales Polonici Mathematici

The existence of a solution for a class of quasilinear integrodifferential equations of Volterra-Hammerstein type with nonlinear boundary conditions is established. Such equations occur in the study of the p-Laplace equation, generalized reaction-diffusion theory, non-Newtonian fluid theory, and in the study of turbulent flows of a gas in a porous medium. The results are obtained by using upper and lower solutions, and extend some previously known results.

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