Irene Benedetti, Department of Mathematics and Informatics, University of Perugia, I-06123, Perugia, Italy, e-mail: irene.benedetti@dmi.unipg.it; Luisa Malaguti, Dept. of Engineering Sciences and Methods, University of Modena and Reggio Emilia, I-42122 Reggio Emilia, Italy, e-mail: luisa.malaguti@unimore.it; Valentina Taddei, Dept. of Pure and Applied Mathematics, University of Modena and Reggio Emilia, I-41125 Modena, Italy, e-mail: valentina.taddei@unimore.it
Abstract: 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.
Keywords: multivalued boundary value problem, differential inclusion in Banach space, compact operator, fixed point theorem
Classification (MSC 2010): 34G25, 34B15
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