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ON THE EXISTENCE OF FIXED-SIGN SOLUTIONS FOR A SYSTEM OF GENERALIZED RIGHT FOCAL PROBLEMS WITH DEVIATING ARGUMENTS

By Patricia J. Y. Wong

Abstract

Abstract. We consider the following system of third-order three-point generalized right focal boundary value problems u ′′′ i (t) = fi(t, u1(φ1(t)), u2(φ2(t)), · · · , un(φn(t))), t ∈ [a, b] ui(a) = u ′ i (zi) = 0, γiui(b) + δiu ′′ i (b) = 0 where i = 1, 2, · · · , n, 1 2 (a + b) < zi < b, γi ≥ 0, δi> 0, and φi are deviating arguments. By using some fixed point theorems, we establish the existence of one or more fixed-sign solutions u = (u1, u2, · · · , un) for the system, i.e., for each 1 ≤ i ≤ n, θiui(t) ≥ 0 for t ∈ [a, b], where θi ∈ {1, −1} is fixed. An example is also presented to illustrate the results obtained. 1. Introduction. I

Topics: u i (t) = fi(t, u1(φ1(t, u2(φ2(t, · · ·, un(φn(t, t ∈ [a, b
Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.360.1354
Provided by: CiteSeerX
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