Positive solutions of elliptic systems with superlinear nonlinearities on the boundary
Abstract
We consider elliptic systems with superlinear and subcritical boundary conditions and a bifurcation parameter as a multiplicative factor. By combining the rescaling method with degree theory and elliptic regularity theory, we prove the existence of a connected branch of positive weak solutions that bifurcates from infinity as the parameter approaches zero. Furthermore, under additional conditions on the nonlinearities near zero, we obtain a global connected branch of positive solutions bifurcating from zero, which possesses a unique bifurcation point from infinity when the parameter is zero. Finally, we analyze the behavior of this branch and discuss the number of positive weak solutions with respect to the parameter using bifurcation theory, degree theory, and sub- and super-solution methods.
Keywords
Cite
@article{arxiv.2511.04943,
title = {Positive solutions of elliptic systems with superlinear nonlinearities on the boundary},
author = {Shalmali Bandyopadhyay and Maya Chhetri and Briceyda Delgado and Nsoki Mavinga and Rosa Pardo},
journal= {arXiv preprint arXiv:2511.04943},
year = {2025}
}