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.
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Acknowledgements
This research was supported by the Slovenian Research Agency grants P1-0292, J1-8131, J1-7025, N1-0064, and N1-0083. V.D. Rădulescu acknowledges the support through a grant of the Romanian Ministry of Research and Innovation, CNCS–UEFISCDI, Project Number PN-III-P4-ID-PCE-2016-0130, within PNCDI III.
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Papageorgiou, N.S., Rădulescu, V.D. & Repovš, D.D. Double-phase problems with reaction of arbitrary growth. Z. Angew. Math. Phys. 69, 108 (2018). https://doi.org/10.1007/s00033-018-1001-2
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DOI: https://doi.org/10.1007/s00033-018-1001-2