Sufficient and necessary conditions for the existence of positive solutions with finite energy for elliptic systems in exterior domains
DOI:
https://doi.org/10.12775/TMNA.2025.035Keywords
Minimal solutions, solutions with finite energy, sub- and supersolutions methods, exterior domainsAbstract
We discuss the existence and nonexistence of positive decaying solutions for a semilinear elliptic systems considered in an exterior domain. Applying the subsolutions and supersolutions method and the Sattinger's iteration schema we prove that our problem possesses solutions with minimal growth and finite energy in a neighborhood of infinity. We also formulate necessary conditions for the existence of such solutions for a certain class of nonlinearities. Finally, some nonexistence results are formulated.References
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