For the following Neumann problem in a ball {-Delta(p)u + u(p-1) = u(q-1) in B, u > 0, u radial in B, partial derivative u/partial derivative nu = 0 on partial derivative B, with 1 < p < q < infinity, we prove continuous dependence on p, for radially nondecreasing solutions. As a byproduct, we obtain an existence result for nonconstant solutions in the case p is an element of (1,2) and q larger than an explicit threshold.
CONTINUOUS DEPENDENCE FOR p-LAPLACE EQUATIONS WITH VARYING OPERATORS / Colasuonno, Francesca; Noris, Benedetta; Sovrano, Elisa. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 18:6(2025), pp. 1561-1573. [10.3934/dcdss.2024121]
CONTINUOUS DEPENDENCE FOR p-LAPLACE EQUATIONS WITH VARYING OPERATORS
Sovrano, Elisa
2025
Abstract
For the following Neumann problem in a ball {-Delta(p)u + u(p-1) = u(q-1) in B, u > 0, u radial in B, partial derivative u/partial derivative nu = 0 on partial derivative B, with 1 < p < q < infinity, we prove continuous dependence on p, for radially nondecreasing solutions. As a byproduct, we obtain an existence result for nonconstant solutions in the case p is an element of (1,2) and q larger than an explicit threshold.
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