# A viability result for nonconvex semilinear functional differential inclusions

Vasile Lupulescu; Mihai Necula

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2005)

- Volume: 25, Issue: 1, page 109-128
- ISSN: 1509-9407

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topVasile Lupulescu, and Mihai Necula. "A viability result for nonconvex semilinear functional differential inclusions." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 25.1 (2005): 109-128. <http://eudml.org/doc/271517>.

@article{VasileLupulescu2005,

abstract = {We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.},

author = {Vasile Lupulescu, Mihai Necula},

journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},

keywords = {viability; invariance; tangency condition; semilinear differential inclusions},

language = {eng},

number = {1},

pages = {109-128},

title = {A viability result for nonconvex semilinear functional differential inclusions},

url = {http://eudml.org/doc/271517},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Vasile Lupulescu

AU - Mihai Necula

TI - A viability result for nonconvex semilinear functional differential inclusions

JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization

PY - 2005

VL - 25

IS - 1

SP - 109

EP - 128

AB - We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.

LA - eng

KW - viability; invariance; tangency condition; semilinear differential inclusions

UR - http://eudml.org/doc/271517

ER -

## References

top- [1] J.P. Aubin, Viability Theory. Systems & Control: Foundations & Applications, Birkhäuser Boston, Inc., Boston, MA 1991.
- [2] R.J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12. Zbl0163.06301
- [3] H. Brézis and F.E. Browder, A general principle on ordered sets in nonlinear functional analysis, Advances in Math. 21 (3) (1976), 355-364. Zbl0339.47030
- [4] C. Castaing and M.D.P. Monteiro Marques, Topological properties of solution sets for sweeping processes with delay, Portugal. Math. 54 (4) (1997), 485-507. Zbl0895.34053
- [5] O. Cârja and M.D.P. Monteiro Marques, Viability for nonautonomous semilinear differential equations, J. Differential Equations 166 (2) (2000), 328-346. Zbl0966.34053
- [6] O. Cârja and C. Ursescu, The characteristics method for a first order partial differential equation, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 39 (4) (1993), 367-396. Zbl0842.34021
- [7] O. Cârja and I.I. Vrabie, Some new viability results for semilinear differential inclusions, NoDEA Nonlinear Differential Equations Appl. 4 (3) (1997), 401-424.
- [8] K. Deimling, Multivalued differential equations, De Gruyter Series in Nonlinear Analysis and Applications, 1. Walter de Gruyter & Co., Berlin 1992.
- [9] W.E. Fitzgibbon, Semilinear functional differential equations in Banach space, J. Differential Equations 29 (1) (1978), 1-14. Zbl0392.34041
- [10] A. Fryszkowski, Existence of solutions of functional-differential inclusion in nonconvex case, Ann. Polon. Math. 45 (2) (1985), 121-124. Zbl0579.34049
- [11] A. Gavioli and L. Malaguti, Viable solutions of differential inclusions with memory in Banach spaces, Portugal. Math. 57 (2) (2000), 203-217. Zbl0963.34059
- [12] L. Górniewicz, Topological fixed point theory of multivalued mappings, Mathematics and its Applications, 495. Kluwer Academic Publishers, Dordrecht 1999. Zbl0937.55001
- [13] G. Haddad, Monotone trajectories of differential inclusions and functional-differential inclusions with memory, Israel J. Math. 39 (1-2) (1981), 83-100. Zbl0462.34048
- [14] G. Haddad, Monotone viable trajectories for functional-differential inclusions, J. Differential Equations 42 (1) (1981), 1-24. Zbl0472.34043
- [15] J.K. Hale and S.M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, 99. Springer-Verlag, New York 1993.
- [16] F. Iacob and N.H. Pavel, Invariant sets for a class of perturbed differential equations of retarded type, Israel J. Math. 28 (3) (1977), 254-264. Zbl0366.34057
- [17] M. Kisielewicz, Differential inclusions and optimal control, Mathematics and its Applications (East European Series), 44, Kluwer Academic Publishers Group, Dordrecht; PWN-Polish Scientific Publishers, Warsaw 1991.
- [18] V. Lakshmikantham and S. Leela, Nonlinear differential equations in abstract spaces, International Series in Nonlinear Mathematics: Theory, Methods and Applications, 2, Pergamon Press, Oxford-New York 1981. Zbl0456.34002
- [19] V. Lakshmikantham, S. Leela and V. Moauro, Existence and uniqueness of solutions of delay differential equations on a closed subset of a Banach space, Nonlinear Anal. 2 (3) (1978), 311-327. Zbl0384.34040
- [20] S. Leela and V. Moauro, Existence of solutions in a closed set for delay differential equations in Banach spaces, Nonlinear Anal. 2 (1) (1978), 47-58. Zbl0383.34053
- [21] V. Lupulescu and M. Necula, Viability and local invariance for non-convex semilinear differential inclusions, Nonlinear Funct. Anal. Appl. 9 (3) (2004), 495-512. Zbl1073.34077
- [22] E. Mitidieri and I.I. Vrabie, A class of strongly nonlinear functional differential equations, Universita degli Studi di Trieste, Instituto di Matematica, Quaderni Matematici II Serie 122 (1986), 1-19.
- [23] E. Mitidieri and I.I. Vrabie, Existence for nonlinear functional differential equations, Hiroshima Math. J. 17 (3) (1987), 627-649.
- [24] N.H. Pavel, Differential equations, flow invariance and applications, Research Notes in Mathematics, 113, Pitman (Advanced Publishing Program), Boston, MA 1984.
- [25] A. Syam, Contribution Aux Inclusions Différentielles, Doctoral thesis, Université Montpellier II, 1993.
- [26] A.A. Tolstonogov and I.A. Finogenko, On functional differential inclusions in Banach space with a nonconvex right-hand side, Soviet. Math. Dokl. 22 (1980), 320-324.
- [27] I.I. Vrabie, C₀-semigroups and applications, North-Holland Mathematics Studies, 191, North-Holland Publishing Co., Amsterdam 2003.
- [28] G.F. Webb, Autonomous nonlinear functional differential equations and nonlinear semigroups, J. Math. Anal. Appl. 46 (1974), 1-12. Zbl0277.34070
- [29] Q.J. Zhu, On the solution set of differential inclusions in Banach space, J. Differential Equations 93 (2) (1991), 213-237. Zbl0735.34017

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