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|Thesis Advisor||Let f [0, I] R R be function satisfying Caratheodory’s conditions and e(t) L[0, 1]. Let r/( (0,1), ’, (0,1), a, >_ 0, 1,2,- ,m- 2, with ,,2 ai 1, 0 < f < f2 < < ,-2 < be given. This paper is concerned with the problem of existence of a solution for the following boundary value problems x"(t) f(t,z(t),z’(t)) + (t),O < < 1, x’(O) O, x(1) x(r/), :"() =/(t, :(), :’())+ (t),o < < , x’(0) 0, x() ET a,x(,). Conditions for the existence of a solution for the above boundary -alue problems are given using Leray Schauder Continuation theorem. Keywords and Phrases: three-point boundary value problem, m-point boundary value problem, Leray Schauder Continuation theorem, Caratheodory’s conditions, Arzela-Ascoli Theorem. AMS(MOS) Subject Classification: 34B10, 34B15, 34(320.|
|Author||Gupta, Chaitan P.|
|Date of Issue||1995|
|Description||Let f:[0,1]×R2?R be function satisfying Caratheodory's conditions and e(t)?L1[0,1]. Let ??(0,1), ?i?(0,1), ai?0, i=1,2,…,m?2, with ?i=1m?2ai=1, 0<?1<?2<…<?m?2<1 be given. This paper is concerned with the problem of existence of a solution for the following boundary value problems x?(t)=f(t,x(t),x?(t))|
|Rights||Creative Commons Attribution 4.0 United States|
|Title||Existence theorems for a second order m-point boundary value problem at resonance|