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Positive doubly periodic solutions of nonlinear telegraph equations

✍ Scribed by Yongxiang Li

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
125 KB
Volume
55
Category
Article
ISSN
0362-546X

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✦ Synopsis

This paper deals with the existence of nontrivial doubly periodic solutions for the nonlinear telegraph equation

where c ΒΏ 0 is a constant, a; b ∈ C(R 2 ; R + ), f ∈ C(R 2 Γ— R + ; R + ), and a; b; f are 2 -periodic in t and x. We show the existence of positive doubly periodic weak solutions when 0 6 a(t; x) 6 c 2 =4 and f is either superlinear or sublinear on u by using the Krasnoselskii's ΓΏxed point theorem in cones.

πŸ“œ SIMILAR VOLUMES

Positive periodic solutions of Hill’s eq
Positive periodic solutions of Hill’s equations with singular nonlinear perturbations
✍ Jifeng Chu; Ming Li πŸ“‚ Article πŸ“… 2008 πŸ› Elsevier Science 🌐 English βš– 278 KB

We study the existence and multiplicity of positive periodic solutions of Hill's equations with singular nonlinear perturbations. The new results are applicable to the case of a strong singularity as well as the case of a weak singularity. The proof relies on a nonlinear alternative principle of Ler