Qualitative behavior of global solutions to some nonlinear fourth order differential equations

DOI10.1016/j.jde.2011.05.036zbMath1236.34042OpenAlexW2007473420MaRDI QIDQ640039

Paschalis Karageorgis, Alberto Ferrero, Elvise Berchio, Gazzola, Filippo

Publication date: 12 October 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.05.036

zbMATH Keywords

growthboundednessoscillation of solutionsenergy functioncontinuation of solutionshomoclinicsfourth order semilinear ordinary differential equation

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Growth and boundedness of solutions to ordinary differential equations (34C11) Asymptotic properties of solutions to ordinary differential equations (34D05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

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Cites Work

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• Existence and stability of entire solutions to a semilinear fourth order elliptic problem
• Homoclinic solutions for Swift-Hohenberg and suspension bridge type equations
• Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity
• The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity
• Large-amplitude periodic oscillations in simple and complex mechanical system: outgrowths from nonlinear analysis
• The existence of ground states for fourth-order wave equations
• Multiplicity of solutions for a fourth order problem with exponential nonlinearity
• Traveling waves in a nonlinearly suspended beam: Theoretical results and numerical observations
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• A note on a class of higher order conformally covariant equations
• Multitransition kinks and pulses for fourth order equations with a bistable nonlinearity
• Hardy-Rellich inequalities with boundary remainder terms and applications
• A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam
• Quasilinear Dirichlet problems driven by positive sources
• Sequential Buckling: A Variational Analysis
• Structural localization phenomena and the dynamical phase-space analogy
• Travelling Waves in a Suspension Bridge
• Homoclinic orbits in the dynamic phase-space analogy of an elastic strut
• A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
• Stable Solutions for the Bilaplacian with Exponential Nonlinearity

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