Existence Results for Third-Order Differential Inclusions with Three-Point Boundary Value Problems
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Abstract
In this paper, we investigate the solutions for a third-order dif-ferential inclusion with three-point boundary value problem. In the rst we applying the Schaefers xed point theorem combined with a selection theorem due to Bressan and Colombo. And in the second our result is based on the xed point theorem for multivalued maps due to Covitz and Nadler.
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Rezaiguia, A., & Kelaiaia, S.
(2016).
Existence Results for Third-Order Differential Inclusions with Three-Point Boundary Value Problems.
Acta Mathematica Universitatis Comenianae, 85(2), 311-318.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/250/392
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References
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[2] A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Mathematica, vol. 90, no. 1, pp. 69-86, 1988.
[3] Covitz, H. and Nadler S. B. Jr.: Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 8, (1970), 5-11.
[4] J. P. Aubin and A. Cellina, Differential Inclusions. Springer-Verlag.
[5] G. V. Smirnov, Introduction to the Theory of Di¤erential Inclusions, vol. 41 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2002.
[6] J. Simsen and C. B. Gentile, Systems of p-Laplacian di¤erential inclusions with large diffusion, Journal of Mathematical Analysis and Applications, vol. 368, no. 2, pp. 525-537, 2010.
[7] M. Kisielewicz, Differential Inclusions and Optimal Control, vol. 44 of Mathematics and Its Applications (East European Series), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.
[8] J. P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhauser, Boston (1990).
[9] K. Deimling, Multivalued Di¤erential Equations. Walter De Gruyter, Berlin-New York (1992).
[10] L. G´orniewicz, Topological Fixed Point Theory of Multivalued Map pings. Mathematics and Its Applications 495, Kluwer Academic Publishers, Dordrecht (1999).
[11] S. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Volume I: Theory. Kluwer Academic Publishers, Dordrecht-Boston-London (1997).
[12] F.J. Torres, Positive Solution For A Third-Order three point boundary value Problem, Electronic Journal of Differential Equations, Vol. 2013 (2013), No. 147, pp. 1-11.
[13] Frigon, M. and Granas, A.: Théorèmes d'existence pour des inclusions di¤érentielles sans convexité, C. R. Acad. Sci. Paris, Ser. I., 310, (1990), 819-822.
[14] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977.