Solvability of multipoint boundary value problems at resonance for higher-order ordinary differential equations
Let f : [0, 1] x R-n --> R be a continuous function and e is an element of L-1 [0, 1]. Let beta(j) (1 less than or equal to j less than or equal to m - 2) is an element of R, 0 < n(1), < eta(2) < (...) < eta(m-2) < 1 be given. This paper is concerned with the existence of solutions for the following n(th)-order multipoint boundary value problems at resonance case x((n)) (t) = f (t, x (t), x' (t), ..., x((n-1)) (t)), + e(t) t is an element of(0, 1), x (0) = x' (0) = ... = x((n-2)) (0) = 0, x (1) = Sigma(j=1)(m=2) beta(j)x(eta(j)). and x((n)) (t) = f (t, x (t), x' (t), ..., x((n-1)) (t)), + e(t) t is an element of(0, 1), x (0) = x' (0) = ... = x((n-2)) (0) = 0, x (1) = Sigma(j=1)(m=2) beta(j)x'(eta(j)). Some existence results are obtained by using the coincidence degree theory of Mawhin. (C) 2005 Elsevier Ltd. All rights reserved.
multipoint boundary value problem resonance coincidence degree theory