The index of a critical point for nonlinear elliptic operators with strong coefficient growth

DOI10.2969/jmsj/05210109zbMath0953.47042OpenAlexW2156616979MaRDI QIDQ1975894

Athanassios G. Kartsatos, Igor V. Skrypnik

Publication date: 27 August 2000

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2969/jmsj/05210109

zbMATH Keywords

Sobolev spaceboundary value problemsdegree theoryindex formulanonlinear elliptic PDEsbifurcation problems\((S_{+})\)-operatorsindex of an isolated critical pointnonlinear operators with strong coefficient growth

Mathematics Subject Classification ID

Equations involving nonlinear operators (general) (47J05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Degree theory for nonlinear operators (47H11) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Abstract bifurcation theory involving nonlinear operators (47J15) Bifurcations in context of PDEs (35B32)

Related Items (10)

Degree theory for \((S_+)\) mappings in non-reflexive Banach spaces ⋮ Topological degree theories and nonlinear operator equations in Banach spaces ⋮ The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces ⋮ A new topological degree theory for perturbations of the sum of two maximal monotone operators ⋮ The index of a critical point for densely defined operators of type (𝑆₊)_{𝐿} in Banach spaces ⋮ On the homotopy property of topological degree for maximal monotone mappings ⋮ Coincidence degree theory for mappings of classL − (S₊) ⋮ Constrained topological degree and positive solutions of fully nonlinear boundary value problems ⋮ A note on the degree for maximal monotone mappings in finite dimensional spaces ⋮ Ranges of densely defined generalized pseudomonotone perturbations of maximal monotone operators.

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