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Antiperiodic solutions for semilinear evolution equations

✍ Scribed by Yuqing Chen; Yeol Je Cho; Jong Soo Jung

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
393 KB
Volume
40
Category
Article
ISSN
0895-7177

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✦ Synopsis

In this paper, we study the existence problem of antiperiodic solutions for the following first-order semilinear evolution equation:

in a Hilbert space H, where A is a self-adjoint operator, OG is the gradient of G. Existence results are obtained under assumptions that D(A) is compactly embedded into H and 0G is continuous or G is a convex function, which extend some known results in [1,2].

πŸ“œ SIMILAR VOLUMES

Integral Inequalities and Global Solutio
Integral Inequalities and Global Solutions of Semilinear Evolution Equations
✍ Milan MedvedΜ† πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 86 KB

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.

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✍ Hirokazu Oka; Naoki Tanaka πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 259 KB

## Abstract The Cauchy problem for the abstract semilinear evolution equation __u__^β€²^(__t__) = __Au__ (__t__) + __B__ (__u__ (__t__)) + __C__ (__u__ (__t__)) is discussed in a general Banach space __X__. Here __A__ is the so‐called Hille‐Yosida operator in __X__, __B__ is a differentiable operator