Electron. J. Diff. Equ., Vol. 2015 (2015), No. 171, pp. 1-12.

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

Syrine Masmoudi, Samia Zermani

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.

Submitted February 2, 2015. Published June 22, 2015.
Math Subject Classifications: 34B18, 35J66.
Key Words: p-Laplacian problem; positive solution; boundary behavior; Schauder fixed point theorem

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Syrine Masmoudi
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: syrine.sassi@fst.rnu.tn
Samia Zermani
Département de Mathématiques, Faculté des Sciences de Tunis
Campus Universitaire, 2092 Tunis, Tunisia
email: zermani.samia@yahoo.fr

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