Analytical and numerical results for the Fučík spectrum of the Laplacian.

DOI10.1016/j.cam.2003.06.003zbMath1049.65127OpenAlexW2041706665MaRDI QIDQ1421201

D. Massart

Publication date: 26 January 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.06.003

zbMATH Keywords

algorithmNewton's methodLaplace equationFučík spectrumBifurcationMountain pass algorithmVariational formulation

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Variational methods for second-order elliptic equations (35J20) Bifurcations in context of PDEs (35B32)

Related Items

Constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems, Bifurcation surfaces stemming from the Fučik spectrum, Infinitely many new curves of the Fučík spectrum, On the Fucík spectrum, Existence of type (II) regions and convexity and concavity of potential functionals corresponding to jumping nonlinear problems, THE QUANTITATIVE ANALYSIS ON THE FUCÍK SPECTRUM AND SOLVABILITY OF JUMPING NONLINEAR PROBLEMS, Nontrivial Fučík spectrum of one non-selfadjoint operator, On a class of optimal partition problems related to the Fučík spectrum and to the monotonicity formulae, Variational properties of the first curve of the Fučík spectrum for elliptic operators, Localization of Fučík curves for the second order discrete Dirichlet operator, On the Fučík spectrum of the Laplacian on a torus, A note on the relation between the Fučík spectrum and Pareto eigenvalues

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On nontrivial solutions of a Dirichlet problem whose jumping nonlinearity crosses a multiple eigenvalue
• Some remarks on the number of solutions of some nonlinear elliptic problems
• A deformation lemma on a \(C^ 1\) manifold
• On the first curve of the Fučik spectrum of an elliptic operator
• Type (II) regions between curves of the Fučik spectrum
• On the resonance set in a fourth-order equation with jumping nonlinearity
• Computing eigenvalues and Fučik-spectrum of the radially symmetric \(p\)-Laplacian
• Radial Fučik spectrum of the Laplace operator
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• Structure of the Fučík spectrum and existence of solutions for equations with asymmetric nonlinearities
• Semilinear elliptic problem with crossing of multiple eigenvalues
• Résultats d'existence et de non-existence pour certains problèmes demi-linéaires à l'infini
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• On the periodic Fučik spectrum and a superlinear Sturm–Liouville equation
• A remark on the resonance set for a semilinear elliptic equation
• A generic property of the resonance set of an elliptic operator with respect to the domain
• A mountain pass method for the numerical solution of semilinear elliptic problems