TY - JOUR

T1 - Global bifurcation for 2mth-order boundary value problems and infinitely many solutions of superlinear problems

AU - Rynne, Bryan P.

PY - 2003/3/1

Y1 - 2003/3/1

N2 - We consider the boundary value problem Lu(x) = p(x)u(x) + g(x, u(0)(x),...,u(2m-1)(x))u(x), x?(0,p), (*) where (i) L is a 2mth order, self-adjoint, disconjugate ordinary differential operator on [0, p], together with separated boundary conditions at 0 and p; (ii) p is continuous and p = 0 on [0, p], while p ? 0 on any interval in [0, p]; (iii) g: [0, p] × R2m ?R is continuous and there exist increasing functions ?u, ?l : [0, 8) ? [0, 8) such that with limt?8 ?l(t) = 8 (the non-linear term in (*) is superlinear as u(x) ? 8). We obtain a global bifurcation result for a related bifurcation problem. We then use this to obtain infinitely many solutions of (*) having specified nodal properties. © 2002 Elsevier Science (USA). All rights reserved.

AB - We consider the boundary value problem Lu(x) = p(x)u(x) + g(x, u(0)(x),...,u(2m-1)(x))u(x), x?(0,p), (*) where (i) L is a 2mth order, self-adjoint, disconjugate ordinary differential operator on [0, p], together with separated boundary conditions at 0 and p; (ii) p is continuous and p = 0 on [0, p], while p ? 0 on any interval in [0, p]; (iii) g: [0, p] × R2m ?R is continuous and there exist increasing functions ?u, ?l : [0, 8) ? [0, 8) such that with limt?8 ?l(t) = 8 (the non-linear term in (*) is superlinear as u(x) ? 8). We obtain a global bifurcation result for a related bifurcation problem. We then use this to obtain infinitely many solutions of (*) having specified nodal properties. © 2002 Elsevier Science (USA). All rights reserved.

UR - http://www.scopus.com/inward/record.url?scp=0037373875&partnerID=8YFLogxK

U2 - 10.1016/S0022-0396(02)00146-8

DO - 10.1016/S0022-0396(02)00146-8

M3 - Literature review

VL - 188

SP - 461

EP - 472

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -