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Existence and uniqueness of solutions for a nonlinear second order differential equation in Hilbert space

Published online by Cambridge University Press:  20 January 2009

Dang Dinh Hai
Dang Dinh Hai
Affiliation:
Department of Mathematics, Dai Hoc Tong Hop, Hochiminh City University, Vietnam
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Abstract

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This paper is concerned with the existence and uniqueness of solutions for the Picard boundary value problem

in a real Hilbert space. Our theorems improve corresponding results of Mawhin for |k| large.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 89 - 95
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Hai, Dang Dinh, On the existence of periodic solutions for Lienard's equation, Math. Nachr. 139 (1988), 245–249.CrossRefGoogle Scholar
2.Mawhin, J., Topological Degree Methods in Nonlinear Boundary Value Problems (Regional Conf. Series in Math. 40, Amer. Math. Soc. Providence, R.I., 1979).Google Scholar
3.Mawhin, J., Two point boundary value problems for nonlinear second order differential equations in Hilbert spaces, Tôhoku Math. J. 32 (1980), 225–233.CrossRefGoogle Scholar