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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.

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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