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Existence theorems for a second order m-point boundary value problem at resonance
Gupta - 1995 - Existence theorems for a second order m-point boun.pdf
Gupta - 1995 - Existence theorems for a second order m-point boun.pdf (2.211Mb)
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.