Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
hyperbolic differential inclusions; fixed point; solution set
hyperbolic differential inclusions; fixed point; solution set
Summary:
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
References:
[1] F. S. De Blasi and J. Myjak: On the set of solutions of a differential inclusion. Bull. Inst. Math. Acad. Sinica 14 (1986), 271–275. MR 0866561
[2] F. S. De Blasi and J. Myjak: On the structure of the set of solutions of the Darboux problem of hyperbolic equations. Proc. Edinburgh Math. Soc. 29 (1986), 7–14. MR 0829175
[3] F. S. De Blasi, G. Pianigiani and V. Staicu: On the solution sets of some nonconvex hyperbolic differential inclusions. Czechoslovak Math. J. 45 (1995), 107–116. MR 1314533
[4] L. Gorniewicz and T. Pruszko: On the set of solutions of the Darboux problem for some hyperbolic equations. Bull. Acad. Polon. Sci. Math. Astronom. Phys. 38 (1980), 279–285. MR 0620202
[5] S. Marano: Generalized solutions of partial differential inclusions depending on a parameter. Rend. Accad. Naz. Sci. Mem. Mat. 107 (1989), 281–295. MR 1041756 | Zbl 0702.35168
[6] S. Marano: Fixed points of multivalued contractions with nonclosed, nonconvex values. Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 5 (1994), 203–212. MR 1298263 | Zbl 0862.54040
[7] S. Marano and V. Staicu: On the set of solutions to a class of nonconvex nonclosed differential inclusions. Acta Math. Hungar. 76 (1997), 287–301. DOI 10.1023/A:1006533606338 | MR 1459237
[8] S. Marano and V. Staicu: Correction to the paper On the set of solutions to a class of nonconvex nonclosed differential inclusions. Acta Math. Hungar. 78 (1998), 267–268. DOI 10.1023/A:1006539007972 | MR 1604707
[9] V. Staicu: On a non-convex hyperbolic differential inclusion. Proc. Edinburgh Math. Soc. 35 (1992), 375–382. MR 1187000 | Zbl 0769.34018
[10] G. Teodoru: A characterization of the solutions of the Darboux problem for the equation $u_{xy}\in F(x,y,u)$. An. Stiint. Univ. Al. I. Cuza Iasi Mat. 33 (1987), 33–38. MR 0925687
Search
Partner of
