Positive radial solutions to a 'semilinear' equation involving the Pucci's operator

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Abstract

In this article we prove existence of positive radially symmetric solutions for the nonlinear elliptic equation A formula is presented. where Mλ,Λ+ denotes the Pucci's extremal operator with parameters 0 < λ ≤ Λ and BR is the ball of radius R in RN, N ≥ 3. The result applies to a wide class of nonlinear functions f, including the important model cases: (i) γ = 1 and f (s) = sp, 1 <p <p*+. (ii) γ = 0, f (s) = αs + sp, 1 <p <p*+ and 0 ≤ α < μ1+. Here p*+ is critical exponent for Mλ,Λ+ and μ1+, is the first eigenvalue of Mλ,Λ+ in BR. Analogous results are obtained for the operator Mλ,Λ-. © 2004 Published by Elsevier Inc.

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Felmer, P. L., & Quaas, A. (2004). Positive radial solutions to a “semilinear” equation involving the Pucci’s operator. Journal of Differential Equations, 199(2), 376–393. https://doi.org/10.1016/j.jde.2004.01.001

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