Nikolaos Socrates Papageorgiou (Author), Vicenţiu Rǎdulescu (Author), Dušan Repovš (Author)

Abstract

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.

Keywords

double-phase problem;nonlinear maximum principle;nonlinear regularity theory;critical point theory;critical groups;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UL FMF - Faculty of Mathematics and Physics
UDC: 517.956.2
COBISS: 18409561 Link will open in a new window
ISSN: 0044-2275
Views: 519
Downloads: 293
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Other data

Type (COBISS): Article
Pages: art. 108 (21 str.)
Volume: ǂVol. ǂ69
Issue: ǂiss. ǂ4
Chronology: Aug. 2018
DOI: 10.1007/s00033-018-1001-2
ID: 11206832