| Title:
|
Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem (English) |
| Author:
|
Benedetti, Irene |
| Author:
|
Malaguti, Luisa |
| Author:
|
Taddei, Valentina |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
367-375 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper deals with the multivalued boundary value problem $x'\in A(t,x)x+F(t,x)$ for a.a.\ $t \in [a,b]$, $Mx(a)+Nx(b) =0$, in a separable, reflexive Banach space $E$. The nonlinearity $F$ is weakly upper semicontinuous in $x$. We prove the existence of global solutions in the Sobolev space $W^{1,p}([a,b], E)$ with $1<p<\infty $ endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion. (English) |
| Keyword:
|
multivalued boundary value problem |
| Keyword:
|
differential inclusion in Banach space |
| Keyword:
|
compact operator |
| Keyword:
|
fixed point theorem |
| MSC:
|
34A60 |
| MSC:
|
34B15 |
| MSC:
|
34G25 |
| idZBL:
|
Zbl 1249.34171 |
| idMR:
|
MR2985546 |
| DOI:
|
10.21136/MB.2011.141696 |
| . |
| Date available:
|
2011-11-10T15:49:26Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141696 |
| . |
| Reference:
|
[1] Andres, J., Malaguti, L., Taddei, V.: On boundary value problems in Banach spaces.Dyn. Syst. Appl. 18 (2009), 275-301. Zbl 1195.34091, MR 2543232 |
| Reference:
|
[2] Basova, M. M., Obukhovski, V. V.: On some boundary value problems for functional-differential inclusions in Banach spaces.J. Math. Sci. 149 (2008), 1376-1384. MR 2336427, 10.1007/s10958-008-0071-7 |
| Reference:
|
[3] Benedetti, I., Malaguti, L., Taddei, V.: Semilinear differential inclusions via weak topologies.J. Math. Anal. Appl. 368 (2010), 90-102. Zbl 1198.34109, MR 2609261, 10.1016/j.jmaa.2010.03.002 |
| Reference:
|
[4] Benedetti, I., Malaguti, L., Taddei, V.: Two-point b.v.p. for multivalued equations with weakly regular r.h.s.Nonlinear Analysis, Theory Methods Appl. 74 (2011), 3657-3670. Zbl 1221.34161, MR 2803092 |
| Reference:
|
[5] Castaing, C., Valadier, V.: Convex Analysis and Measurable Multifunctions.Lect. Notes Math. 580, Springer, Berlin (1977). Zbl 0346.46038, MR 0467310, 10.1007/BFb0087688 |
| Reference:
|
[6] Daleckiĭ, Ju. L., Kreĭn, M. G.: Stability of Solutions of Differential Equations in Banach Spaces.Translation of Mathematical Monographs, American Mathematical Society, Providence, R. I. (1974). MR 0352639 |
| Reference:
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[7] Edwards, R. E.: Functional Analysis: Theory and Applications.Holt Rinehart and Winston, New York (1965). Zbl 0182.16101, MR 0221256 |
| Reference:
|
[8] Kamenskii, M. I., Obukhovskii, V. V., Zecca, P.: Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Space.W. de Gruyter, Berlin (2001). MR 1831201 |
| Reference:
|
[9] Marino, G.: Nonlinear boundary value problems for multivaued differential equations in Banach spaces.Nonlinear Anal., Theory Methods Appl. 14 (1990), 545-558. MR 1044285, 10.1016/0362-546X(90)90061-K |
| . |
