On nonresonance for systems of semilinear wave equations

DOI10.1016/S0362-546X(96)00067-3zbMath0887.35013WikidataQ126464426 ScholiaQ126464426MaRDI QIDQ4346007

Vesa Mustonen, Juha Berkovits

Publication date: 28 July 1997

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

weak solutionsnonresonance conditionsgeneralized degree

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Second-order nonlinear hyperbolic equations (35L70) Degree theory for nonlinear operators (47H11)

Related Items (9)

Nonnegative doubly periodic solutions for nonlinear telegraph system with twin-parameters ⋮ Multiplicity results of periodic solutions for a coupled system of wave equations ⋮ Periodic solutions to Klein-Gordon systems with linear couplings ⋮ Existence and multiplicity results of positive doubly periodic solutions for nonlinear telegraph system ⋮ Nonnegative doubly periodic solutions for nonlinear telegraph system ⋮ On the Leray-Schauder formula and bifurcation ⋮ Periodic solutions of telegraph-wave coupled system at nonresonance ⋮ Three positive doubly periodic solutions of a nonlinear telegraph system ⋮ Resonance in nonlinear wave equations with \(x\)-dependent coefficients

Cites Work

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• An extension of Leray-Schauder degree and applications to nonlinear wave equations
• Conservative systems of semi-linear wave equations with periodic Dirichlet boundary conditions
• On the unique solvability of semi-linear operator equations in Hilbert spaces
• Iterative and variational methods for the solvability of some semilinear equations in Hilbert spaces
• Existence and uniqueness for a variational hyperbolic system without resonance
• Topological Degree and Multiplication Theorem for a Class of Nonlinear Mappings

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