Solutions of nonlinear hyperbolic equations at resonance

DOI10.1016/0362-546X(82)90063-3zbMath0495.35007OpenAlexW1979454587MaRDI QIDQ3958799

Rangachary Kannan, Lamberto Cesari

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0362-546x(82)90063-3

zbMATH Keywords

existenceSchauder's fixed point theoremresonancebifurcation equationalternative methodlocal resultssemi-linear hyperbolic equationsreduction to an alternative problemsemilinear abstract operators

Mathematics Subject Classification ID

Periodic solutions to PDEs (35B10) Fixed-point theorems (47H10) Second-order nonlinear hyperbolic equations (35L70) Higher-order nonlinear hyperbolic equations (35L75)

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Cites Work

• Nonlinear oscillations across a point of resonance for nonselfadjoint systems
• The implicit function theorem in functional analysis
• Periodic solutions of a class of hyperbolic equations containing a small parameter
• Existence in the large of periodic solutions of hyperbolic partial differential equations
• On the existence of periodic solutions for the equations \(D_{tt}u + (-1)^{p} D_{x}^{2p} u = \varepsilon f(\cdot,\cdot,u)\)
• Periodic solutions of a class of weakly nonlinear evolution equations
• An Abstract Existence Theorem at Resonance
• Generalized periodic solutions of nonlinear telegraph equations
• Functional analysis and nonlinear differential equations
• Equivalent Norms for Sobolev Spaces
• Periodic solutions of the equation $u_{tt}+u_{xxxx}=\varepsilon f(\cdot,\cdot,u,u_t)$
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