In this peqwr, tlw author uses the methods in [I, 2] to study tile existence of ,~ohttions of three ~mini houndarv vahte problems.[or mmlinear fottrth order d(fferential CtIIHIIiOll tl ~ --" [(t, Y, Y', Y", Y'" ) (~) with the I~otltt(hllT conditions g(ll(a) ,Yt(a) ,YtP(a), Y~lt(a)) = 0, h(y(b),ytr(b
A three point boundary value problem for nonlinear fourth order differential equations
โ Scribed by John R. Graef; Chuanxi Qian; Bo Yang
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 211 KB
- Volume
- 287
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
โฆ Synopsis
In this paper, the authors consider the nonlinear fourth order ordinary differential equation
with the boundary conditions
Some results on the existence and nonexistence of positive solutions to problem (E)-(B) are obtained. Results on the existence of infinitely many positive solutions are also presented. Examples are included to demonstrate that the results are sharp.
๐ SIMILAR VOLUMES
A fourth-order accurate finite difference method is developed for a class of fourth order nonlinear two-point boundary value problems. The method leads to a pentadiagonal scheme in the linear cases, which often arise in the beam deflection theory. The convergence of the method is tested numerically