On the Fucík spectrum

DOI10.1016/j.jde.2008.02.021zbMath1148.35055OpenAlexW2161498629MaRDI QIDQ924835

Zhaoli Liu, Chong Li, Pan, Jian Zhong, Shu-Jie Li

Publication date: 19 May 2008

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

Full work available at URL: https://doi.org/10.1016/j.jde.2008.02.021

zbMATH Keywords

differentiabilitysolvabilityimplicit function theoremnodal domainFucík curveFucík spectrumhomotopy index

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) General topics in linear spectral theory for PDEs (35P05) Variational methods for second-order elliptic equations (35J20)

Related Items (11)

Elliptic equations with jumping nonlinearities involving high eigenvalues ⋮ Basis properties of Fučik eigenfunctions ⋮ The Fučík spectrum of Schrödinger operator and the existence of four solutions of Schrödinger equations with jumping nonlinearities ⋮ Bifurcation surfaces stemming from the Fučik spectrum ⋮ Least energy solutions of the Schrödinger-Kirchhoff equation with linearly bounded nonlinearities ⋮ Infinitely many new curves of the Fučík spectrum ⋮ Nonresonance conditions on the potential with respect to the Fučík spectrum for semilinear Dirichlet problems ⋮ Existence of type (II) regions and convexity and concavity of potential functionals corresponding to jumping nonlinear problems ⋮ On Schechter's linking theorems ⋮ Dancer-Fučik spectrum for fractional Schrödinger operators with a steep potential well on \(\mathbb{R}^N\) ⋮ Variational properties of the first curve of the Fučík spectrum for elliptic operators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Saddle points and multiple solutions of differential equations
• On positive solutions of some pairs of differential equations. II
• Some remarks on the number of solutions of some nonlinear elliptic problems
• Partial regularity of the zero-set of solutions of linear and superlinear elliptic equations
• On the existence of solutions of certain asymptotically homogeneous problems
• Critical point theory and Hamiltonian systems
• Type II regions between curves of the Fučik spectrum and critical groups
• Generic domain dependence for non-smooth equations and the open set problem for jumping nonlinearities
• On the first curve of the Fučik spectrum of an elliptic operator
• Type (II) regions between curves of the Fučik spectrum
• Analytical and numerical results for the Fučík spectrum of the Laplacian.
• Splitting theorem, Poincaré--Hopf theorem and jumping nonlinear problems
• Infinite dimensional Morse theory and multiple solution problems
• Multiple solutions of asymptotically homogeneous problems
• Structure of the Fučík spectrum and existence of solutions for equations with asymmetric nonlinearities
• Résultats d'existence et de non-existence pour certains problèmes demi-linéaires à l'infini
• Boundary value problems with jumping nonlinearities
• Boundary-value problems for weakly nonlinear ordinary differential equations
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• A generic property of the resonance set of an elliptic operator with respect to the domain
• Half-eigenvalues of elliptic operators
• Generic properties of the Fucik spectrum of elliptic operators

This page was built for publication: On the Fucík spectrum