This paper is devoted to the study of semi-stable radial solutions u H¹ (B₁) of -Δu= x^αf (u) in B₁0, where f C¹ (R) is a general nonlinearity, α>-2 and B₁ is the unit ball of RN, N>1. We establish the boudness of such solutions for dimensions 2 N<10+4α and sharp pointwise estimates in the case N10+4α. In addition, we provide, for this range of dimensions, a large family of semi-stable radially decreasing unbounded H¹ (B₁) solutions.
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Martínez-Baena et al. (Thu,) studied this question.
www.synapsesocial.com/papers/68f04acce559138a1a06e99b — DOI: https://doi.org/10.48550/arxiv.2506.21515
J. Silverio Martínez-Baena
Salvador Villegas
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