Sufficient and necessary conditions for the existence of positive solutions with finite energy for elliptic systems in exterior domains - Orpel, Aleksandra (Topological Methods in Nonlinear Analysis, 2026)
We discuss the existence and nonexistence of positive decaying solutions for asemilinear elliptic systems considered in an exterior domain.Applying thesubsolutions and supersolutions method and the Sattinger's iteration schema weprove that our problem possesses solutions with minimal growth and finiteenergy in a neighborhood of infinity.We also formulate necessary conditionsfor the existence of such solutions for a certain class of nonlinearities.Finally, some nonexistence results are formulated.