Displaying similar documents to “Existence theory for nonlinear Volterra integral and differential equations.”

Weak and strong topologies and integral equations in Banach spaces

Donal O'Regan (1995)

Annales Polonici Mathematici

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The Schauder-Tikhonov theorem in locally convex topological spaces and an extension of Krasnosel’skiĭ’s fixed point theorem due to Nashed and Wong are used to establish existence of L α and C solutions to Volterra and Hammerstein integral equations in Banach spaces.

On monotonic solutions of an integral equation of Abel type

Mohamed Abdalla Darwish (2008)

Mathematica Bohemica

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We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C [ 0 , 1 ] . The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk (1992)

Annales Polonici Mathematici

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A differential equation of the form (q(t)k(u)u')' = λf(t)h(u)u' depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.