On Discontinuous Implicit Evolution Equations

Journal of Mathematical Analysis and Applications

Volumn 219, Issue 2, 1998, Pages 455-471

  Carl, S ^a   Heikkila S ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b UNIVERSITY OF OULU   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002040331     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1997.5832     Document Type: Article

References (32)

1. Appel J., Zabrejko P. P. Nonlinear Superposition Operators. 1990;Cambridge Univ. Press. Cambridge.
2. Arendt W., Favini A. Integrated solutions to implicit differential equations. Rend. Sem. Mat. Univ. Politec. Torino. 51:1993;315-329.
3. Bajic V. B. Nonlinear functions and stability of motions of implicit differential systems. Internat. J. Control. 52:1990;1167-1187.
4. Barbu V., Favini A. Existence for implicit differential equations in Banach spaces. Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 3:1992;203-215.
5. Barbu V., Favini A. Convergence of solutions of implicit differential equations. Differential Integral Equations. 7:1994;665-688.
6. Brull L., Pallaske U. On differential algebraic equations with discontinuities. Z. Angew. Math. Phys. 43:1992;319-327.
7. S. Carl, S. Heikkilä, Pirkko, Koponen, On first order discontinuous implicit boundary value problems, Dynam. Control Discr. Imp. Syst.
8. Frigon M., Kaczynski T. Boundary value problems for systems of implicit differential equations. J. Math. Anal. Appl. 179:1993;317-326.
9. Heikkilä S. On the quasimonotonicity of linear differential systems. Appl. Anal. 10:1980;121-126.
10. Heikkilä S. On the quasimonotonicity of differential systems. Nonlinear Anal. 7:1983;91-96.
11. Heikkilä S. First order discontinuous implicit differential equations with discontinuous boundary conditions. Nonlinear Anal. 30:1997;1753-1761.
12. Heikkilä S., Lakshmikantham V. Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations. 1994;Dekker, New York.
13. Hokkanen V. M. Continuous dependence for an implicit nonlinear equation. J. Differential Equations. 110:1994;67-85.
14. Hokkanen V. M. Existence of a periodic solution for implicit nonlinear equations. Differential Integral Equations. 9:1996;745-760.
15. Jankowski T. A numerical solution of implicit ODE. Demonstratio Math. 25:1992;279-295.
16. Kaczynski T., Krawcewics W. A local Hopf bifurcation theorem for a certain class of implicit differential equations. Canad. Math. Bull. 36:1993;183-189.
17. Krasnosel'skii M. A. Positive Solutions of Operator Equations. 1961;Noordhoff, Groningen.
18. Kravtsov P. A. The Cauchy problem and implicit equations. Partial Differential Equations Leningrad Gos. Ped. Inst. Leningrad. 1990.
19. Kravtsov P. A. Existence and uniqueness of the solution of the Cauchy problem for an implicit system of differential equations. Differential Equations (Qualitative Theory) Ryazan Gos. Ped. Inst. Ryazan. 1990.
20. Krein S. G., Utochkina E. O. An implicit canonical equation in a Hilbert space. Ukrainian Math. J. 42:1990;345-347.
21. Marusyak A. G. Determination of the periodic solution of systems of first order ordinary differential equations that are not solved with respect to the derivative. Akad. Nauk Ukrain. SSR Inst. Mat. Kiev. 1984;43-53.
22. Niepage H. D. On the Numerical Solution of Differential-Algebraic Equations with Discontinuities. 1991;Teubner, Stuttgart. p. 108-116.
23. Prosenyuk L. G. Representation of regular solutions of a real differential equation that is not solved with respect to the derivative. Izv. Vyssh. Uchebn. Zaved. Mat. 1990;70-72.
24. Prosenyuk L. G. On the existence and asymptotic properties of a real system of differential equations that are not solved with respect to the derivative. Ukrainian Math. J. 45:1993;1644-1648.
25. Rabier P. J. Implicit differential equations near a singular point. J. Math. Anal. Appl. 2:1989;425-449.
26. Rabier P. J., Rheinboldt W. C. A geometric treatment of implicit algebraic equations. J. Differential Equations. 109:1994;110-146.
27. Rabier P. J., Rheinboldt W. C. On impasse points of quasilinear differential-algebraic equations. J. Math. Anal. Appl. 181:1994;429-454.
28. Redheffer R. M., Walter W. Remarks on ordinary differential equations in ordered Banach spaces. Monatsh. Math. 102:1986;237-249.
29. Ricceri B. Solutions lipschiziennes d'equations différentielles sous forme implicite. C. R. Acad. Sci. Paris Sér. I Math. 295:1982;245-248.
30. Saint-Raymond J. Equations différentielles sous implicite. Matematiche (Catania). 2:1989;237-257.
31. Vakhidov S. Existence and uniqueness of the solution of a differential equation, which cannot be solved with respect to the derivative, in a normed space. Dokl. Akad. Nauk UzSSR. 11:1987;13-15.
32. Zernov A. E. The existence and asymptotic behavior of the solution of the Cauchy problem of implicit form. Izv. Vyssh. Uchebn. Zaved. Mat. 1:1993;78-81.