▫$(p,2)$▫-equations asymmetric at both zero and infinity

Papageorgiou, Nikolaos S. (author), Rǎdulescu, Vicenţiu (author), Repovš, Dušan (author)

We consider a ▫$(p,2)$▫-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a ▫$p$▫-Laplacian and a Laplacian with ▫$p>2$▫. The reaction term is ▫$(p-1)$▫-linear, but exhibits asymmetric behavior at ▫$\pm \infty$▫ and at ▫$0^\pm$▫. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal).

• Language: English
• Keywords: asymmetric reaction, resonance, Fučik spectrum, constant sign solutions, nodal solution, critical groups, Morse relation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2018
• Number of pages: Str. 327-351
• Numbering: Vol. 7, iss. 3
• PID: 20.500.12556/RUL-109201
• UDC: 517.956.2
• ISSN on article: 2191-9496
• DOI: 10.1515/anona-2017-0195
• COBISS.SI-ID: 18174297
• Publication date in RUL: 26.08.2019

Record is a part of a journal

• Title: Advances in nonlinear analysis
• Publisher: De Gruyter
• ISSN: 2191-9496
• COBISS.SI-ID: 16253785