Spectral Theory for Linear Operators of Mixed Type and Applications to Nonlinear Dirichlet Problems

DOI10.1080/03605302.2012.686549zbMath1388.35130OpenAlexW1964072432MaRDI QIDQ5200544

Kevin R. Payne, Daniela Lupo, Dario Daniele Monticelli

Publication date: 6 November 2012

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605302.2012.686549

zbMATH Keywords

bifurcationspectral theorynonlinear boundary value problemstopological methodsmixed type PDE

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) PDEs of mixed type (35M10) Bifurcations in context of PDEs (35B32) Topological and monotonicity methods applied to PDEs (35A16)

Related Items (7)

On Tricomi problem of Chaplygin's hodograph equation ⋮ Variational Characterizations of Weak Solutions to the Dirichlet Problem for Mixed-Type Equations ⋮ Estimates of singular numbers (s$$ s $$‐numbers) and eigenvalues of a mixed elliptic‐hyperbolic type operator with parabolic degeneration ⋮ On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains ⋮ On the degenerate hyperbolic Goursat problem for linear and nonlinear equations of Tricomi type ⋮ Nonexistence of nontrivial generalized solutions for 2-D and 3-D BVPs with nonlinear mixed type equations ⋮ On the Dirichlet problem of mixed type for lower hybrid waves in axisymmetric cold plasmas

Cites Work

• Spectral bounds for Tricomi problems and application to semilinear existence and existence with uniqueness results
• Maximum principles for weak solutions of degenerate elliptic equations with a uniformly elliptic direction
• On cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations
• An embedding theorem for sobolev spaces related to non-smooth vector fieldsand harnack inequality
• Critical exponents for semilinear equations of mixed elliptic‐hyperbolic and degenerate types
• MIXED EQUATIONS AND TRANSONIC FLOW
• On closed boundary value problems for equations of mixed elliptic‐hyperbolic type

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