A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type

Soohyun Bae

Address: Department of Mathematical Sciences, Hanbat National University, Daejeon 34158, Republic of Korea

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Abstract: We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present the proof of the local existence of positive radial solutions near $0$ under suitable conditions on $K$. Moreover, we provide a priori estimates of positive radial solutions near $\infty $ when $r^{-\ell }K(r)$ for $\ell \ge -p$ is bounded near $\infty $.

AMSclassification: primary 35J92; secondary 35B45.

Keywords: quasilinear equation, positive solution, a priori bound.

DOI: 10.5817/AM2023-2-155