On the existence of fixed-sign solutions for a system of generalized right focal problems with deviating arguments
Patricia J.Y. Wong - School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore (email) Abstract: 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
Keywords: Fixed-sign solutions, system of boundary value problems, right focal.
Received: August 2006; Revised: February 2007; Published: September 2007. |