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2007, 2007(Special): 1042-1051. doi: 10.3934/proc.2007.2007.1042

On the existence of fixed-sign solutions for a system of generalized right focal problems with deviating arguments

1. 

School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Received  August 2006 Revised  February 2007 Published  September 2007

We consider the following system of third-order three-point generalized right focal boundary value problems

$u^(''')_ i (t) = f_i(t, u_1(\phi_1(t)), u_2(\phi_2(t)), · · · , u_n(\phi_n(t))), t \in [a, b]$ $u_i(a) = u^'_i(z_i) = 0$, \gamma_i u_i(b) + \delta_iu^('')_i (b) = 0$

where $i$ = 1, 2, · · · , $n$, $1/2 (a + b) < z_i < b, \gamma_i > 0$, and $\phi_i$ are deviating arguments. By using some fixed point theorems, we establish the existence of one or more fixed-sign solutions $u = (u_1, u_2, · · · , u_n)$ for the system, i.e., for each 1 $<=$ $i$ $<=$ $n$, $\theta_iui(t) >= 0$ for $t \in [a, b]$, where $\theta_i \in$ {1,−1} is fixed. An example is also presented to illustrate the results obtained.

Citation: Patricia J.Y. Wong. On the existence of fixed-sign solutions for a system of generalized right focal problems with deviating arguments. Conference Publications, 2007, 2007 (Special) : 1042-1051. doi: 10.3934/proc.2007.2007.1042
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