Second and third order boundary value problems

Schrader, Keith

doi:10.1090/S0002-9939-1972-0291548-4

Second and third order boundary value problems
HTML articles powered by AMS MathViewer

by Keith Schrader PDF

Proc. Amer. Math. Soc. 32 (1972), 247-252 Request permission

Abstract:

In this paper some existence theorems for solutions on $( - \infty , + \infty )$ of second and third order differential equations of the form $y'' = f(t,y,y’)$ and $y''’ = f(t,y,y’,y'')$ are established. The hypotheses include the assumption that f is continuous, that solutions of initial value problems extend to $( - \infty , + \infty )$ and that certain boundary value problems have no more than one solution.

References

J. W. Bebernes, A subfunction approach to a boundary value problem for ordinary differential equations, Pacific J. Math. 13 (1963), 1053–1066. MR 156018
Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
Lloyd Jackson and Keith Schrader, Existence and uniqueness of solutions of boundary value problems for third order differential equations, J. Differential Equations 9 (1971), 46–54. MR 269920, DOI 10.1016/0022-0396(70)90152-X
Lloyd Jackson and Keith Schrader, Subfunctions and third order differential inequalities, J. Differential Equations 8 (1970), 180–194. MR 257525, DOI 10.1016/0022-0396(70)90044-6
È. G. Halikov, On the question of existence of bounded solutions of a differential equation of second order, Differencial′nye Uravnenija 2 (1966), 1668–1670 (Russian). MR 0206367
Keith Schrader, A note on second order differential inequalities, Proc. Amer. Math. Soc. 19 (1968), 1007–1012. MR 234097, DOI 10.1090/S0002-9939-1968-0234097-0
Keith W. Schrader, Existence theorems for second order boundary value problems, J. Differential Equations 5 (1969), 572–584. MR 239175, DOI 10.1016/0022-0396(69)90094-1