Existence of solutions of abstract fractional integrodifferential equations of Sobolev type
โ Scribed by Balachandran, K.; Kiruthika, S.
- Book ID
- 119211424
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 220 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0898-1221
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๐ SIMILAR VOLUMES
In this paper, we establish a set of sufficient conditions for the existence of mild solutions of nonlinear neutral integrodifferential equations in Banach spaces by using the Schaefer fixed-point theorem. An application is provided to illustrate the theory.
Sufficient conditions for the global existence of a strong solution of the equation \(u_{t}(t, x)=\int_{0}^{i} k(t-s) \sigma\left(u_{x}(s, x)\right)_{x} d s+f(t, x)\) are given. The kernel \(k\) satisfies \(9 \hat{k}(z) \geqslant\) \(\kappa|\exists \hat{k}(z)|\) and \(\sigma\) is increasing with \(\