论文信息 - Existence of solutions for a class of third-order nonlinear boundary value problems

Existence of solutions for a class of third-order nonlinear boundary value problems

Abstract In this paper, we are concerned with the following third-order ordinary differential equation: x‴(t)+f t,x(t),x′(t),x″(t) =0, 0 with the nonlinear boundary conditions x(0)=0, g x′(0),x″(0) =A, h x′(1),x″(1) =B, where A , B ∈ R , f :[0,1]×R 3 →R is continuous, g , h : R 2 → R are continuous. The existence result is given by using a priori estimate, Nagumo condition, upper and lower solutions and Leray–Schauder degree, and we give an example to demonstrate our result.

[1] Ravi P. Agarwal,et al. A uniqueness and Existence theorem for a singular third-order boundary value Problem on [0, infinity) , 2002, Applied Mathematics Letters.

[2] Yuqiang Feng,et al. The existence of solution for a third-order two-point boundary value problem , 2002, Appl. Math. Lett..

[3] Jozef Rovder. On monotone solution of the third-order differential equation , 1996 .

[4] L. Peletier,et al. Two problems from draining flows involving third-order ordinary differential equations , 1996 .

[5] Feliz Minhós,et al. Existence result for some third order separated boundary value problems , 2001 .

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

[7] Alberto Cabada,et al. Extremality and comparison results for discontinuous implicit third order functional initial-boundary value problems , 2003, Appl. Math. Comput..

[8] Eva Rovderová. Third-order boundary-value problem with nonlinear boundary conditions , 1995 .