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;
2024-01-01
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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