scholarly journals Periodic solutions of semilinear wave equations with discontinuous nonlinearities

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
In-Sook Kim ◽  
Jung-Hyun Bae ◽  
Suk-Joon Hong
Keyword(s):  
Periodic Solutions ◽  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Discontinuous Nonlinearities

scholarly journals Rotationally invariant periodic solutions of semilinear wave equations

1998 ◽  
Vol 3 (1-2) ◽  
pp. 171-180 ◽  
Author(s):  
Martin Schechter
Keyword(s):  
Wave Equation ◽  
Periodic Solutions ◽  
Essential Spectrum ◽  
Wave Operator ◽  
Wave Equations ◽  
Periodic Case ◽  
Linear Wave ◽  
Semilinear Wave Equations ◽  
Semilinear Wave Equation ◽  
Rotationally Invariant

Under suitable conditions we are able to solve the semilinear wave equation in any dimension. We are also able to compute the essential spectrum of the linear wave operator for the rotationally invariant periodic case.

Nonlinear problems with strong resonance at infinity: an abstract theorem and applications

1985 ◽  
Vol 99 (3-4) ◽  
pp. 333-345 ◽  
Author(s):  
A. Capozzi ◽  
A. Salvatore
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Wave Equations ◽  
Nonlinear Problems ◽  
Abstract Theorem ◽  
Semilinear Wave Equations ◽  
Strong Resonance ◽  
Image Position

SynopsisIn this paper, we consider the equationwhere A is a linear operator, N = ψ′ with ψ ∈ C1(E, R), and E is an Hilbert space. We suppose that N has a derivative at infinity N′(∞) and that 0 belongs to the spectrum of A–N′(∞). We prove an abstract theorem for multiplicity of solutions for the above equation. We then apply this theorem to the study of periodic solutions of Hamiltonian systems and of semilinear wave equations when the period is prescribed.

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