# Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem

Irene Benedetti; Luisa Malaguti; Valentina Taddei

Mathematica Bohemica (2011)

- Volume: 136, Issue: 4, page 367-375
- ISSN: 0862-7959

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topBenedetti, Irene, Malaguti, Luisa, and Taddei, Valentina. "Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem." Mathematica Bohemica 136.4 (2011): 367-375. <http://eudml.org/doc/196940>.

@article{Benedetti2011,

abstract = {The paper deals with the multivalued boundary value problem $x^\{\prime \}\in A(t,x)x+F(t,x)$ 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.},

author = {Benedetti, Irene, Malaguti, Luisa, Taddei, Valentina},

journal = {Mathematica Bohemica},

keywords = {multivalued boundary value problem; differential inclusion in Banach space; compact operator; fixed point theorem; multivalued boundary value problem; differential inclusion in Banach space; compact operator; fixed point theorem},

language = {eng},

number = {4},

pages = {367-375},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem},

url = {http://eudml.org/doc/196940},

volume = {136},

year = {2011},

}

TY - JOUR

AU - Benedetti, Irene

AU - Malaguti, Luisa

AU - Taddei, Valentina

TI - Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem

JO - Mathematica Bohemica

PY - 2011

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 136

IS - 4

SP - 367

EP - 375

AB - The paper deals with the multivalued boundary value problem $x^{\prime }\in A(t,x)x+F(t,x)$ 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.

LA - eng

KW - multivalued boundary value problem; differential inclusion in Banach space; compact operator; fixed point theorem; multivalued boundary value problem; differential inclusion in Banach space; compact operator; fixed point theorem

UR - http://eudml.org/doc/196940

ER -

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