Multiplicity results for semilinear elliptic boundary value problems in Besov and Triebel-Lizorkin spaces

DOI10.1017/S0013091500005174zbMath0757.35017OpenAlexW2159461189MaRDI QIDQ3985495

Lassi Päivärinta, Thomas Runst

Publication date: 27 June 1992

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

Full work available at URL: https://doi.org/10.1017/s0013091500005174

zbMATH Keywords

traceDirichlet boundary value problemexistence of solutionLeray-Schauder degreeTriebel-Lizorkin spacefunction space of Besov typesecond-order uniformly elliptic, formally selfadjoint linear operator

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Boundary value problems for second-order elliptic equations (35J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (1)

Singularities in Quasi‐Banach Spaces with Applications to Semilinear Elliptic Equations I

Cites Work

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• Shrinkable neighborhoods in Hausdorff linear spaces
• Theory of function spaces
• Mapping properties of nonlinear operators in spaces of Triebel-Lizorkin and Besov type
• On the admissibility of function spaces of type \(B^ s_{p,q}\) and \(F^ s_{p,q}\), and boundary value problems for non-linear partial differential equations
• On the number of solutions of a nonlinear Dirichlet problem
• On a superlinear elliptic boundary value problem
• On the inversion of some differentiable mappings with singularities between Banach spaces
• Remarks on some quasilinear elliptic equations
• Nonlinear Integral Equations of the Hammerstein Type
• Compact Linear Operators in Linear Topological Spaces

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