A note on divergence-like $2$-point boundary value problems
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- by M. Joshi PDF
- Proc. Amer. Math. Soc. 42 (1974), 547-550 Request permission
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
- Wayne T. Ford, On the first boundary value problem for $[h(x,\,x^{\prime } ,\,t)]^{\prime } =$ $f(x,\,x^{\prime } ,\,t)$, Proc. Amer. Math. Soc. 35 (1972), 491–498. MR 308506, DOI 10.1090/S0002-9939-1972-0308506-3
- Felix E. Browder, Problèmes nonlinéaires, Séminaire de Mathématiques Supérieures, No. 15 (Été, vol. 1965, Les Presses de l’Université de Montréal, Montreal, Que., 1966 (French). MR 0250140 —, 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.
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 547-550
- MSC: Primary 34B15
- DOI: https://doi.org/10.1090/S0002-9939-1974-0328183-7
- MathSciNet review: 0328183