Existence and asymptotic behavior of solutions to nonlinear radial p-Laplacian equations

Abstract

This article concerns the existence, uniqueness and boundary behavior of positive solutions to the nonlinear problem $$\displaylines{ \frac{1}{A}(A\Phi _p(u'))'+a_1(x)u^{\alpha_1}+a_2(x)u^{\alpha_2}=0, \quad \text{in } (0,1), \cr \lim_{x\to 0}A\Phi _p(u')(x)=0,\quad u(1)=0, }$$ where $p>1$, $\alpha _1,\alpha _2\in (1-p,p-1)$, $\Phi_p(t)=t|t|^{p-2}$, $t\in \mathbb{R}$, $A$ is a positive differentiable function and $a_1,a_2$ are two positive measurable functions in $(0,1)$ satisfying some assumptions related to Karamata regular variation theory.

Keywords

• p-Laplacian problem
• positive solution
• boundary behavior
• Schauder fixed point theorem