Positive solutions for nonlinear systems of third-order generalized sturm-liouville boundary value problems with $(p_1,p_2,ldots,p_n)$-laplacian

Abstract

In this work, by<br />employing the Leggett-Williams fixed point theorem, we study the<br />existence of at least three positive solutions of boundary value<br />problems for system of third-order ordinary differential equations<br />with $(p_1,p_2,ldots,p_n)$-Laplacian<br />begin{eqnarray*}<br />left { begin{array}{ll} (phi_{p_i}(u_i''(t)))' + a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0 leq t leq 1,<br /> alpha_i u_i(0) - beta_i u_i'(0) = mu_{i1} u_i(xi_i),hspace{0.2cm}<br /> gamma_i u_i(1) + delta_i u_i'(1) = mu_{i2} u_i(eta_i), hspace{0.5cm}<br /> u_i''(0) = 0,<br />end{array} right.<br />end{eqnarray*}<br />where $ phi_{p_i}(s) = |s|^{p_i-2}s,$, are $p_i$-Laplacian<br />operators, $p_i > 1, 0 < xi_i < 1, 0 < eta_i < 1$ and $mu_{i1},<br />mu_{i2}> 0$ for $i = 1,2, ldots,n$.