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

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


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Authors [Persian]

  • م علیمحمدی 1
  • ن نیامرادی 2
1 گروه ریاضی دانشگاه مازندران
2 گروه ریاضی، دانشگاه رازی، کرمانشاه، ایران
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در این مقالهمسئله با مقادیر مرزی اشتورم-لیوویل، قضیه نقطه ثابت، ...

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