Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on divergence-like $ 2$-point boundary value problems

Author: M. Joshi
Journal: Proc. Amer. Math. Soc. 42 (1974), 547-550
MSC: Primary 34B15
MathSciNet review: 0328183
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The method given by Ford [1] for the existence and uniqueness of a solution in $ H_0^1(I)$ for the boundary value problem $ [h(x,x',t)]' = f(x,x',t), x(0) = x(1) = 0$ is shown to be a special case of Browder's method [3] for partial differential equations of generalized divergence form. Also it is shown that the solution of the above boundary value problem in $ H_0^{1,p}(I)$ can be obtained under weaker hypotheses than those assumed by Ford.

References [Enhancements On Off] (What's this?)

  • [1] W. T. Ford, On the first boundary value problem for $ [h(x,x',t)]' = f(x,x',t)$, Proc. Amer. Math. Soc. 35 (1972), 491-498. MR 0308506 (46:7620)
  • [2] F. E. Browder, Problèmes non-linéaires, Séminaire de Mathématiques Supérieures, No. 15 (Été, 1965), Les Presses de l'Université de Montréal, Montréal, Que., 1966. MR 40 #3380. MR 0250140 (40:3380)
  • [3] -, Existence theorems for nonlinear differential equations, Proc. Sympos. Pure Math., vol. 16, Amer. Math. Soc., Providence, R.I., 1970, pp. 1-60. MR 42 #4855.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B15

Retrieve articles in all journals with MSC: 34B15

Additional Information

Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society