Details

Autor(en) / Beteiligte

• Papageorgiou, Nikolaos S.
• Rădulescu, Vicenţiu D.
• Repovš, Dušan D.

Titel

Double-phase problems with reaction of arbitrary growth

Ist Teil von

• Zeitschrift für angewandte Mathematik und Physik, 2018-08, Vol.69 (4), p.1-21, Article 108

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2018

Quelle

SpringerLink

Beschreibungen/Notizen

• 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.