Filippov Lemma for certain differential inclusion of third order

• Autorzy: Bartuzel, G. , Fryszkowski, A.
• Języki publikacji: EN

Abstrakty

EN

We propose a version of the Filippov Lemma for differential inclusions of the type y'" + k2y' is an element of F(x,y) defined on [—1,1] with boundary conditions y(-1)=y(1)=y'(1)=0.

Słowa kluczowe

PL

inkluzja różniczkowa; lemat Fillipova; operatory różniczkowe

EN

differential inclusion; Fillipov Lemma; differential operators

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 2
• Strony: 337-352
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Bartuzel, G.

autor

Fryszkowski, A.

• Faculty of Mathematics and Information Science Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland,

Bibliografia

• [1] J. P. Aubin and A. Cellina, Differential Inclusions, Springer Verlag 1984.
• [2] G. Bartuzel, A. Fryszkowski, Relaxation of the differential inclusions of the Sturm-Liouville type, Demonstratio Math. 30(4) (1997), 953-960.
• [3] G. Bartuzel, A. Fryszkowski, Stability of the principal eigenvalue of the Schroedinger type problems for differential inclusions, Proceedings of the International Conference in Nonlinear Analysis, Toruń 1999.
• [4] G. Bartuzel, A. Fryszkowski, A class of retracts in Lp with some applications to differential inclusions, Discussiones Math. 22 (2002), 213-224.
• [5] M. Benchohra, J. R. Graef, J. Henderson, S. K. Ntouyas, Nonresonance impulsive higher order functional noncovex-valued differential inclusions, Electronic Journal on Qualitative Theory of Differential Equations 2002, No 13, p. 1-13.
• [6] A. Bressan, A. Cellina, A. Fryszkowski, A class of absolute retracts in spaces of integrable functions, Proc. Amer. Math. Soc. 112 (1991), 413-418.
• [7] A. Cernea, On the existence of solutions for a higher order differential inclusions without convexity, Electronic Journal on Qualitative Theory of Differential Equations 2007, No 8, p. 1-8.
• [8] J. Chaay, Sur les équations differéntielles du troisième ordre at d'ordre supérieur dont l'integrale genérale a ses points critiques fixes, Acta Math. 34 (1911), 317-385.
• [9] A. Fryszkowski, Fixed Point Theory for Decomposable Sets, Kluwer 2004.
• [10] H. Hedenmalm, An Hadamard mazimum principle, Journees Eq. Aux derives partieles (1999), CDR115 (CNRS).
• [11] D. Hilbert, R. Courant, Methods of Mathematical Physics, Wiley 1943 (Vol. 1) and 1962 (Vol. 2).