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 resonance, variational eigenvalues, critical groups, nonlinear regularity, multiple solutions, nodal solutions Article (dk_c) 1.01 - Original Scientific Article PEF - Faculty of Education 2018 str. 105-129 Vol. 18, iss. 1 517.956.2 1536-1365 10.1515/ans-2017-0009 18001241 321 261 (0 votes) Voting is allowed only to logged in users. AddThis uses cookies that require your consent. Edit consent...

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Title: Advanced nonlinear studies Adv. nonlinear stud. De Gruyter 1536-1365 15060569