Title: Existence and multiplicity results for a class of semilinear elliptic equations
Authors: Bobkov, Vladimír
Drábek, Pavel
Hernández, Jesus
Citation: BOBKOV, V., DRÁBEK, P., HERNÁNDEZ, J. Existence and multiplicity results for a class of semilinear elliptic equations. Nonlinear Analysis, 2020, roč. 200, č. NOV 2020, s. 1-25. ISSN 0362-546X.
Issue Date: 2020
Publisher: Elsevier
Document type: článek
URI: 2-s2.0-85086362891
ISSN: 0362-546X
Keywords in different language: Existence;Multiplicity;Branches;Positive solutions;Non-Lipschitz nonlinearities;Variational methods;Flat solutions;Compact support solutions.
Abstract in different language: We study the existence and multiplicity of nonnegative solutions, as well as the behavior of corresponding parameter-dependent branches, to the equation −Δu = (1 − u)um − λun in a bounded domain Ω ⊂ RN endowed with the zero Dirichlet boundary data, where 0 < m ≤ 1 and n > 0. When λ > 0, the obtained solutions can be seen as steady states of the corresponding reaction– diffusion equation describing a model of isothermal autocatalytic chemical reaction with termination. In addition to the main new results, we formulate a few relevant conjectures.
Rights: Plný text není přístupný.
© Elsevier
Appears in Collections:Články / Articles (KMA)

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