Geodesic
Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem
Mathematica Bohemica, Tome 136 (2011) no. 4, pp. 367-375
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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
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 $1$ endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion.
DOI : 10.21136/MB.2011.141696
Classification : 34A60, 34B15, 34G25
Keywords: multivalued boundary value problem; differential inclusion in Banach space; compact operator; fixed point theorem 
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Benedetti, Irene; Malaguti, Luisa; Taddei, Valentina. Boundary value problem for differential inclusions in Fréchet spaces with multiple solutions of the homogeneous problem. Mathematica Bohemica, Tome 136 (2011) no. 4, pp. 367-375. doi: 10.21136/MB.2011.141696

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