Existence of solution of some p,q${p,q}$‐Laplacian system under local superlinear conditions

Patricio Cerda, Marco Souto and Pedro Ubilla

Mathematische Nachrichten, 2022, vol. 295, issue 1, 44-57

Abstract: We study existence of positive radial solutions for the following class of quasi‐linear elliptic systems −Δpu=f(|x|,u,v)inB,−Δqv=g(|x|,u,v)inB,(u,v)=(0,0)on∂B,\begin{equation*}\hspace*{13.5pc} \left\lbrace \def\eqcellsep{&}\begin{array}{rcll} -\Delta _p u &=& f(|x|,u,v) & \text{in}\quad B, \\ -\Delta _q v &=& g(|x|,u,v) & \text{in}\quad B, \\ (u,v) &=& (0,0) & \text{on}\quad \partial B, \end{array} \right. \end{equation*}where the nonlinearities f,g∈C(B×[0,+∞)2;[0,+∞))$ f, g \in C\big (B \times [0,+\infty )^2;\,[0,+\infty )\big )$ satisfy some local superlinear property at +∞$+\infty$. Here B is the unity ball in RN${\mathbb {R}}^N$ and 1

Date: 2022
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