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

Alimohammady, M.; Nyamoradi, N.

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

Document Type : Research Articles

Authors

M. Alimohammady ¹
N. Nyamoradi ²

¹ Dept of Math. Univ of Mazandaran University

² Department of Mathematics, Faculty of Sciences Razi University, 67149 Kermanshah, Iran

Abstract

In this work, by
employing the Leggett-Williams fixed point theorem, we study the
existence of at least three positive solutions of boundary value
problems for system of third-order ordinary differential equations
with $(p_1,p_2,ldots,p_n)$-Laplacian
begin{eqnarray*}
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,
alpha_i u_i(0) - beta_i u_i'(0) = mu_{i1} u_i(xi_i),hspace{0.2cm}
gamma_i u_i(1) + delta_i u_i'(1) = mu_{i2} u_i(eta_i), hspace{0.5cm}
u_i''(0) = 0,
end{array} right.
end{eqnarray*}
where $ phi_{p_i}(s) = |s|^{p_i-2}s,$, are $p_i$-Laplacian
operators, $p_i > 1, 0 < xi_i < 1, 0 < eta_i < 1$ and $mu_{i1},
mu_{i2}> 0$ for $i = 1,2, ldots,n$.

Keywords