Double-phase problems with reaction of arbitrary growth

作者：Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dusan D. Repovs · 发表于：Zeitschrift für angewandte Mathematik und Physik · 年份：2018 · DOI：10.1007/s00033-018-1001-2 · 被引用次数：82 · 研究领域：Nonlinear Partial Differential Equations、Advanced Mathematical Modeling in Engineering、Differential Equations and Numerical Methods

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.