Double-phase problems with reaction of arbitrary growth

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

We consider a parametric nonlinear nonhomogeneous elliptic equation, driven by the sum of two differential operators having different structure. The associated energy functional has unbalanced growth and we do not impose any global growth conditions to the reaction term, whose behavior is prescribed only near the origin. Using truncation and comparison techniques and Morse theory, we show that the problem has multiple solutions in the case of high perturbations. We also show that if a symmetry condition is imposed to the reaction term, then we can generate a sequence of distinct nodal solutions with smaller and smaller energies.

• Language: English
• Keywords: double-phase problem, nonlinear maximum principle, nonlinear regularity theory, critical point theory, critical groups
• 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. 1-21
• Numbering: art. 108, iss. 4
• PID: 20.500.12556/RUL-109147
• UDC: 517.956.2
• ISSN on article: 0044-2275
• DOI: 10.1007/s00033-018-1001-2
• COBISS.SI-ID: 18409561
• Publication date in RUL: 23.08.2019

Record is a part of a journal

• Title: Zeitschrift für angewandte Mathematik und Physik
• Shortened title: Z. angew. Math. Phys.
• Publisher: Birkhaeuser Verlag
• ISSN: 0044-2275
• COBISS.SI-ID: 26662656