On a paper of Mawhin on second order differential equations
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.
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.
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.
DłotkoT. (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
Tadeusz Dłotko
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
Instytut Matematyki, Uniwersytet Śląski w Katowicach Poland
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