Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 69, Issue 4, Pages -Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00033-018-1001-2
Keywords
Double-phase problem; Nonlinear maximum principle; Nonlinear regularity theory; Critical point theory; Critical groups
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Funding
- Slovenian Research Agency [P1-0292, J1-8131, J1-7025, N1-0064, N1-0083]
- Romanian Ministry of Research and Innovation, CNCS-UEFISCDI, within PNCDI III [PN-III-P4-ID-PCE-2016-0130]
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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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