Multiple solutions of anticoercive boundary value problems for a class of ordinary differential equations of second order

DOI10.1016/0022-0396(80)90099-6zbMath0417.34039OpenAlexW1982285632MaRDI QIDQ755017

Michael Struwe

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90099-6

zbMATH Keywords

multiple solutionsanticoercive boundary value problemsCaratheodory conditionsexistence of a periodic solution

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10)

Related Items (18)

Generalizations of the Borsuk theorem ⋮ Gaps of consecutive eigenvalues of Laplace operator and the existence of multiple solutions for superlinear elliptic problem ⋮ Multiple homoclinic solutions for a one-dimensional Schrödinger equation ⋮ A continuation approach to superlinear periodic boundary value problems ⋮ Indefinite weight nonlinear problems with Neumann boundary conditions ⋮ Infinitely many solutions of superlinear boundary value problems with rotational symmetry ⋮ A non-autonomous kind of Duffing equation ⋮ Infinitely many critical points for functionals which are not even and applications to superlinear boundary value problems ⋮ Existence of small solutions to a resonant boundary value problem with large nonlinearity ⋮ On the multiplicity of radial solutions to superlinear Dirichlet problems in bounded domains. ⋮ Periodic solutions of Duffing's equations with superquadratic potential ⋮ Homoclinic and heteroclinic solutions for a class of second-order non-autonomous ordinary differential equations: multiplicity results for stepwise potentials ⋮ Critical point theory on partially ordered Hilbert spaces ⋮ Multiplicity results for systems of superlinear second order equations ⋮ A note on the existence of multiple solutions for a class of systems of second order ODEs ⋮ Existence of a periodic solution for superlinear second order ODEs ⋮ CONTINUATION THEOREMS FOR AMBROSETTI-PRODI TYPE PERIODIC PROBLEMS ⋮ Boundary blow-up for differential equations with indefinite weight

Cites Work

• Über die Existenz der Lösungen von Randwertaufgaben bei gewöhnlhichen nichtlinearen Differentialgleichungen zweiter Ordnung
• Nachweis periodischer Lösungen bei gewissen nichtlinearen Schwingungsdifferentialgleichungen
• Characteristic values associated with a class of nonlinear second-order differential equations
• On boundary value problems for superlinear second order differential equations
• Periodic solutions of x+f(x,t)=0 via the Poincaré-Birkhoff theorem
• Some aspects of nonlinear eigenvalue problems
• Periodic solutions of the equation $x(t)+g(x(t))=p(t)$
• Topologie et équations fonctionnelles
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
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