Iterative and variational methods for the solvability of some semilinear equations in Hilbert spaces

DOI10.1016/0022-0396(92)90097-7zbMath0761.34047OpenAlexW2136767038MaRDI QIDQ1196642

Alessandro Fonda, Jean Mawhin

Publication date: 16 January 1993

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

Full work available at URL: https://doi.org/10.1016/0022-0396(92)90097-7

zbMATH Keywords

Dirichlet problemnonlinear equationselfadjoint operatorexistence and uniqueness theoremreal Hilbert space

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Second-order nonlinear hyperbolic equations (35L70)

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Cites Work

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• Saddle points and multiple solutions of differential equations
• Remarks on the dual least action principle
• Eigenfunction methods and nonlinear hyperbolic boundary value problems at resonance
• Critical points of convex perturbations of some indefinite quadratic forms and semilinear boundary value problems at resonance
• Conservative systems of semi-linear wave equations with periodic Dirichlet boundary conditions
• On the unique solvability of semi-linear operator equations in Hilbert spaces
• Critical point theory and Hamiltonian systems
• The periodic-Dirichlet problem for some semilinear wave equations
• An existence theorem for periodically perturbed conservative systems
• Quelques propriétés des opérateurs angle-bornes et n-cycliquement monotones
• Order intervals of self-adjoint linear operators and nonlinear homeomorphisms
• On implicit function theorems and the existence of solutions of non- linear equations
• Non-linear equations of evolution
• On periodically perturbed conservative systems
• Nichtlineare Integralgleichungen vom Hammersteinschen Typ
• On periodic solutions of nonlinear second order vector differential equations
• On periodic solutions of nonconservative systems
• A mini max theorem and applications to nonresonance problems for semilinear equations
• Quadratic forms, weighted eigenfunctions and boundary value problems for non-linear second order ordinary differential equations
• Periodically perturbed conservative systems and a global inverse function theorem
• The existence of periodic solutions for nonlinearly perturbed conservative systems
• Nonconvex minimization problems
• Solutions of nonlinear elliptic systems with meshed spectra
• Existence and uniqueness for a variational hyperbolic system without resonance
• Nonresonance and existence for nonlinear elliptic boundary value problems
• Density of the Range of Potential Operators
• On a class of abstract systems without resonance in a Hilbert space
• Application of a Lemma on Bilinear Forms to a Problem in Nonlinear Oscillations
• Nonlinear Integral Equations of the Hammerstein Type