Abstract
In this paper, the author combines the topological degree theory and the monotone iterative technique to investigate the existence of solutions and also minimal and maximal solutions of the initial value problem for nonlinear integrodifferential equations of mixed type in Banach space. Two main theorems are obtained and two examples are given.
Highlights
In this paper, the author combines the topological degree theory and the monotone iterative technique to investigate the existence of solutions and minimal and maximal solutions of the initial value problem for nonlinear integrodifferential equations of mixed type in Banach space
JOURNAL OF APPLIED MATHEMATICS AND SIMULATION Vol 2, Issue 1, 1989 degree theory and the monotone iterative technique to investigate the existence of solutions and minimal and maximal solutions of the IVP (1)
It is easy to see that the uniform continuity of F on implies
Summary
The author combines the topological degree theory and the monotone iterative technique to investigate the existence of solutions and minimal and maximal solutions of the initial value problem for nonlinear integrodifferential equations of mixed type in Banach space. Let F be uniformly continuous on DXBRXBRXBR for any R > 0, where It is easy to see that the uniform continuity of F on implies DXBRXBRXBR the boundedness of F on and so A is a bounded and continuous operator from C[I,E] into C[I,E].
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