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

Papageorgiou, Nikolaos (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 (dk_c)
• Tipology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Year: 2018
• Number of pages: str. 327-351
• Numbering: Vol. 7, iss. 3
• UDC: 517.956.2
• ISSN on article: 2191-9496
• DOI: 10.1515/anona-2017-0195
• COBISS.SI-ID: 18174297
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Record is a part of a journal

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