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arXiv · 1908.08915

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

Agnieszka Kałamajska·Anna Kosiorek
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Abstract

We consider degenerated nonlinear PDE of elliptic type: $$ - \mathrm{div}(a(|x|)|\nabla w(x)|^{p-2} \nabla w(x)) + h(|x|,w(x),\langle\nabla w(x),\frac{x}{|x|}\rangle)=ϕ(w(x)), $$ where $x$ belongs to the ball in $\bf{R}^n$. Using the argument based on Opial-type inequalities, we investigate qualitative properties of their radial solutions, like e.g. maximum principles, monotonicity, as well as nonexistence of the nontrivial solutions.

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Agnieszka Kałamajska, Anna Kosiorek. 2019-08-23. On maximum principles for radial solutions to nonlinear elliptic PDE's via Opial-type inequalities. https://arxiv.org/abs/1908.08915

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