On the topological degree for mappings of monotone type

DOI10.1016/0362-546X(86)90108-2zbMath0605.47060OpenAlexW2047396263MaRDI QIDQ3743924

Juha Berkovits, Vesa Mustonen

Publication date: 1986

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(86)90108-2

zbMATH Keywords

topological degreenormalizationexistence and uniquenessadditivityhomotopy invarianceLeray-Schauder degreemaps of monotone typenonlinear higher-order elliptic boundary value problemsnonlinear operator equations in reflexive Banach spaces

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Nonlinear boundary value problems for linear elliptic equations (35J65) Equations involving nonlinear operators (general) (47J05) Degree, winding number (55M25)

Related Items (28)

Unilateral Problems for Nonlinearly Elastic Plates and Shallow Shells ⋮ Existence Results for a Dirichlet Boundary Value Problem Involving the p(x)-Laplacian Operator ⋮ A topological degree for operators of generalized \((S_{+})\) type ⋮ On the degree theory for mappings of monotone type and applications ⋮ Existence and uniqueness results for a class of \(p(x)\)-Kirchhoff-type problems with convection term and Neumann boundary data ⋮ On the normalized eigenvalue problems for nonlinear elliptic operators. II ⋮ Extension of the Leray-Schauder degree for abstract Hammerstein type mappings ⋮ A Browder degree theory from the Nagumo degree on the Hilbert space of elliptic super-regularization ⋮ Unnamed Item ⋮ A new topological degree theory for pseudomonotone perturbations of the sum of two maximal monotone operators and applications ⋮ Study of some elliptic system of (p(x),q(x))-Kirchhoff type with convection ⋮ EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF NONLINEAR DEGENERATE PARABOLIC EQUATIONS IN WEIGHTED SOBOLEV SPACE MOHAMED EL OUAARABI, CHAKIR ALLALOU AND SAID MELLIANI ⋮ Nonlinear Elliptic Boundary Value Problems by Topological Degree ⋮ Quasilinear ellipticity and the Dirichlet problem ⋮ On the uniqueness of the Browder degree ⋮ Some existence theorems for the Dirichlet problem for quasilinear elliptic equations ⋮ Nonlinear elliptic problems in weighted variable exponent Sobolev spaces by topological degree ⋮ A new topological degree theory for perturbations of demicontinuous operators and applications to nonlinear equations with nonmonotone nonlinearities ⋮ Degree theory for multivalued (S) type mappings and fixed point theorems ⋮ On the homotopy property of topological degree for maximal monotone mappings ⋮ Coincidence degree theory for mappings of classL − (S₊) ⋮ Degree theory for monotone type mappings in non-reflexive Banach spaces ⋮ Unilateral eigenvalue problems for nonlinearly elastic plates: An approach via pseudo-monotone operators ⋮ Nonresonance conditions for generalised \(\phi\)-Laplacian problems with jumping nonlinearities ⋮ A note on the degree for maximal monotone mappings in finite dimensional spaces ⋮ A new generalization of Browder's degree ⋮ A reduction theorem for the topological degree for mappings of class (𝑆+) ⋮ A remark on the Leray-Lions condition.

Cites Work

• On pseudo-monotone operators and nonlinear noncoercive variational problems on unbounded domains
• Nonlinear functional equations in Banach spaces and elliptic super- regularization
• Perturbed monotone operators
• On the uniqueness of the topological degree
• Degree of mapping for nonlinear mappings of monotone type: Strongly nonlinear mapping
• Degree of mapping for nonlinear mappings of monotone type
• Degree of mapping for nonlinear mappings of monotone type: Densely defined mapping
• Fixed point theory and nonlinear problems

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