Existence, Stability and Oscillation Properties of Slow-Decay Positive Solutions of Supercritical Elliptic Equations with Hardy Potential

Moroz, Vitaly;Van Schaftingen, Jean
(2014) Edinburgh Mathematical Society. Proceedings — Vol. 58, n° 1, p. 255−271 (2015)

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We prove the existence of a family of slow decay positive solutions of a supercritical elliptic equation with Hardy potential in the entire space and study stability and oscillation properties of these solutions. We also establish the existence of a continuum of stable slow decay positive solutions for the relevant exterior Dirichlet problem.
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Moroz, V., & Van Schaftingen, J. (2014). Existence, Stability and Oscillation Properties of Slow-Decay Positive Solutions of Supercritical Elliptic Equations with Hardy Potential. Edinburgh Mathematical Society. Proceedings, 58(1), 255−271. https://doi.org/10.1017/S0013091513000588 (Original work published 2015)