On a paper of Mawhin on second order differential equations

Tadeusz Dłotko

Published: 1997-09-30

Vol. 11 (1997)

On a paper of Mawhin on second order differential equations

Tadeusz Dłotko

Abstract

The first part of the paper deals with classification of solutions to the equations
u" + σg(t,u⁽ⁱ⁾) = 0, i = 0,1; σ² = 1, t≥0.
The second part is devoted to systems of the form
u"(t) = A(t)u⁽ⁱ⁾(t) - g(t,u(h(t)),u'(h(t))), t∈[0,l]
u⁽ⁱ⁾(0) = u⁽ⁱ⁾(1) = 0, i = 0,1.

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Dłotko, T. (1997). On a paper of Mawhin on second order differential equations. Annales Mathematicae Silesianae, 11, 55–66. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14184

References

1. A. Canada, F. Drábek, On semilinear problems with nonlinearities depending only on derivatives, Západočeska Univerzita, Plzen, Preprinty vědeckých praci, 50, 1994.
2. T. Dłotko, Sur l'allure asymptotique des solutions de l'équation différentielle ordinaire du second ordre, Ann. Pol. Math. XI, 1962, 261-272.
3. S. Fucik, Solvability of nonlinear equations and bounary value problems, Reidel, Dordrecht, 1980.
4. A. Granas, R.B. Guenther, J.W. Lee, Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. pures et appl. 70, 1991, 153-196.
5. E. Kamke, Differentialgleichungen, I., Akad. Verlag., Leipzig, 1962.
6. M.A. Krasnosielskij, Topological methods in the theory of nonlinear integral equations, (in Russian), Moscow, 1956.
7. J. Mawhin, Some remarks on semilinear problems at resonance where the nonlinearity depends only on the derivatives, Acta Math. et Inform., Universitatis Ostraviensis 2 (1994), 61-69.
8. J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS, Reg. Conf. nr 40, AMS, 1979. Google Scholar

Vol. 11 (1997)
Published: 1997-09-30

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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