Multiple solutions for a classical problem in the calculus of variations

DOI10.1006/jdeq.1996.0162zbMath0872.49001OpenAlexW2023879401MaRDI QIDQ1817008

T. Tehrani, Nassif Ghoussoub, Ivar Ekeland

Publication date: 15 October 1997

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

Full work available at URL: https://doi.org/10.1006/jdeq.1996.0162

zbMATH Keywords

critical point theorysemicontinuityboundary value problemEuler-Lagrange equationBolza problemunbounded functionals

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving ordinary differential equations (49J15) Optimality conditions for problems involving ordinary differential equations (49K15) Existence theories for free problems in one independent variable (49J05)

Related Items (13)

A quadratic Bolza-type problem in a Riemannian manifold. ⋮ Multiplicity of periodic solutions for a class of second-order perturbed Hamiltonian systems ⋮ Existence of infinitely many solutions for a class of linear perturbed symmetric elliptic problem with nonhomogeneous boundary ⋮ Infinitely many solutions for the nonlinear Schrödinger-Poisson system with broken symmetry ⋮ Infinitely many solutions for quasilinear elliptic equations with lack of symmetry ⋮ Nonlinear boundary value conditions and ordinary differential systems with impulsive effects ⋮ Multiple solutions for semilinear elliptic systems with non-homogeneous boundary conditions ⋮ Index theory, nontrivial solutions, and asymptotically linear second-order Hamiltonian systems ⋮ Multiple solutions for prescribed boundary value problem ⋮ Index theory for linear selfadjoint operator equations and nontrivial solutions for asymptotically linear operator equations ⋮ Multiplicity of solutions for some semi-linear elliptic systems with non-homogeneous boundary conditions ⋮ On the Bolza problem ⋮ Some applications of a perturbative method to elliptic equations with non-homogeneous boundary conditions.

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