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Double-phase problems with reaction of arbitrary growth
Papageorgiou, Nikolaos (Author), Rǎdulescu, Vicenţiu (Author), Repovš, Dušan (Author)

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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.

Language:English
Keywords:double-phase problem, nonlinear maximum principle, nonlinear regularity theory, critical point theory, critical groups
Work type:Article (dk_c)
Tipology:1.01 - Original Scientific Article
Organization:PEF - Faculty of Education
Year:2018
Number of pages:str. 1-21
Numbering:art. 108, iss. 4
UDC:517.956.2
ISSN on article:0044-2275
DOI:10.1007/s00033-018-1001-2 This link opens in a new window
COBISS.SI-ID:18409561 This link opens in a new window
Views:302
Downloads:221
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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 This link opens in a new window

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