论文信息 - Solutions of 2nth Lidstone boundary value problems and dependence on higher order derivatives

Solutions of 2nth Lidstone boundary value problems and dependence on higher order derivatives

Abstract In this paper, we consider the Lidstone boundary value problem (−1) n u (2n) (x)=f x,u(x),u″(x),…,u (2(n−1)) (x) , 0 u (2i) (0)=u (2i) (1)=0, 0⩽i⩽n−1. Some monotone conditions are imposed on f which enable us to apply a new maximum principle to deduce the existence of solution. The emphasis here is that f depends on higher order derivatives. Two examples are also included to dwell upon the importance of the results obtained.

Weigao Ge | Zhanbing Bai | Zhanbing Bai | W. Ge

[1] Zhanbing Bai,et al. The Method of Lower and Upper Solutions for a Bending of an Elastic Beam Equation , 2000 .

[2] Manuel del Pino,et al. Existence for a fourth-order boundary value problem under a two-parameter nonresonance condition , 1991 .

[3] Ravi P. Agarwal,et al. Eigenvalues of Lidstone boundary value problems , 1999, Appl. Math. Comput..

[4] H. Weinberger,et al. Maximum principles in differential equations , 1967 .

[5] A. R. Aftabizadeh. Existence and uniqueness theorems for fourth-order boundary value problems , 1986 .

[6] Zhanbing Bai,et al. On positive solutions of some nonlinear fourth-order beam equations , 2002 .

[7] D. Gilbarg,et al. Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[8] Johann Schröder. Fourth order two-point boundary value problems; estimates by two-sided bounds , 1984 .

[9] Zhang Jihui,et al. The Method of Lower and Upper Solutions for Fourth-Order Two-Point Boundary Value Problems , 1997 .

[10] Ravi P. Agarwal,et al. On fourth order boundary value problems arising in beam analysis , 1989, Differential and Integral Equations.

[11] Alberto Cabada,et al. The Method of Lower and Upper Solutions for Second, Third, Fourth, and Higher Order Boundary Value Problems , 1994 .

[12] John M. Davis,et al. General Lidstone problems : Multiplicity and symmetry of solutions , 2000 .