Lacunary bifurcation for operator equations and nonlinear boundary value problems on ℝN

DOI10.1017/S0308210500029073zbMath0765.47017MaRDI QIDQ3980462

Hans-Peter Heinz

Publication date: 26 June 1992

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

bifurcationcritical point theorystrongly indefinite functionalsnonlinear eigenvalue problemssemilinear elliptic partial differential equationsgaps in the essential spectrumnonlinear perturbations of the periodic Schrödinger equation

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Variational methods for second-order elliptic equations (35J20) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07)

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Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems ⋮ Solvability of nonlinear equations in spectral gaps of the linearization ⋮ Unbounded solution components for nonlinear Hill's equations ⋮ Unnamed Item ⋮ On the Solution Structure of Nonlinear Hill's Equation I, Global Results ⋮ Existence of a Nontrivial Solution to a Strongly Indefinite Semilinear Equation ⋮ On the Solution Structure of Nonlinear Hill's Equation II, Local Results ⋮ Existence and bifurcation of solutions for nonlinear perturbations of the periodic Schrödinger equation ⋮ A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations ⋮ Minimax characterization of solutions for a semilinear elliptic equation with lack of compactness

Cites Work

• Uniqueness and bifurcation for solutions of nonlinear Sturm-Liouville eigenvalue problems
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• Critical point theorems for indefinite functionals
• The lowest point of the continuous spectrum as a bifurcation point
• On perturbations of a translationally-invariant differential equation
• Bifurcation of Homoclinic Orbits and Bifurcation from the Essential Spectrum
• The existence of infinitely many bifurcating branches
• Bifurcation in L^p (R^N ) for a Semilinear Elliptic Equation
• Bifurcation for Dirichlet Problems Without Eigenvalues