On the existence of solutions of certain asymptotically homogeneous problems

DOI10.1007/BF01214337zbMath0438.35023OpenAlexW1980647815MaRDI QIDQ1141829

E. Norman Dancer

Publication date: 1981

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173045

zbMATH Keywords

spectrumLeray-Schauder degreecompact resolventhomotopy indexasymptotic homogeneous problems

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Degree, winding number (55M25) Nonlinear higher-order PDEs (35G20)

Related Items (13)

A remark on the resonance set for a semilinear elliptic equation ⋮ Bifurcation surfaces stemming from the Fučik spectrum ⋮ Infinitely many new curves of the Fučík spectrum ⋮ Existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero ⋮ Competing species systems with diffusion and large interactions ⋮ On the Fucík spectrum ⋮ Fučík spectrum of a singular sturm-liouville problem ⋮ A generic property of the resonance set of an elliptic operator with respect to the domain ⋮ Operators with jumping nonlinearities and combinatorics ⋮ Variational properties of the first curve of the Fučík spectrum for elliptic operators ⋮ Multiple solutions of asymptotically homogeneous problems ⋮ A semilinear problem with jumping nonlinearities in unbounded domains ⋮ On the use of asymptotics in nonlinear boundary value problems

Cites Work

• Saddle points and multiple solutions of differential equations
• On the ranges of certain weakly nonlinear elliptic partial differential equations
• On the inversion of some differentiable mappings with singularities between Banach spaces
• On differentiable functions with isolated critical points
• On the existence of zeros of perturbed operators
• Boundary-value problems for weakly nonlinear ordinary differential equations
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• Some Generalizations of the Borsuk-Ulam Theorem
• A relation between the type numbers of a critical point and the index of the corresponding field of gradient vectors
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