On maximum principles for radial solutions to nonlinear elliptic PDE's\n via Opial-type inequalities

2019/08/23 by Agnieszka Kałamajska, Kałamajska, Agnieszka, Anna Maria Kosiorek +2
Computer Science · Mathematics · #26D10 #35B50 #35J92 #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1908.08915

openalex publication_date 2019/08/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/08/04

Abstract

We consider degenerated nonlinear PDE of elliptic type: \n -
mathrmdiv(a(|x|)|
nabla w(x)|^p-2
nabla w(x)) +\nh(|x|,w(x),
langle
nabla w(x),
fracx|x|
rangle)=
phi(w(x)), where x\nbelongs to the ball in bfRⁿ. Using the argument based on Opial-type\ninequalities, we investigate qualitative properties of their radial solutions,\nlike e.g. maximum principles, monotonicity, as well as nonexistence of the\nnontrivial solutions.\n

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