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Existence and multiplicity of solutions for resonant ▫$(p,2)$▫-equations
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

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Abstract
We consider Dirichlet elliptic equations driven by the sum of a ▫$p$▫-Laplacian ▫$(2 < p)$▫ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both ▫$\pm \infty$▫ and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.

Language:English
Keywords:resonance, variational eigenvalues, critical groups, nonlinear regularity, multiple solutions, nodal solutions
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2018
Number of pages:str. 105-129
Numbering:Vol. 18, iss. 1
UDC:517.956.2
ISSN on article:1536-1365
DOI:10.1515/ans-2017-0009 Link is opened in a new window
COBISS.SI-ID:18001241 Link is opened in a new window
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Downloads:261
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Record is a part of a journal

Title:Advanced nonlinear studies
Shortened title:Adv. nonlinear stud.
Publisher:De Gruyter
ISSN:1536-1365
COBISS.SI-ID:15060569 This link opens in a new window

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