Existence of multiple solutions for a wide class of differential inclusions

We give a unified approach to study the existence of multiple positive solutions of nonlinear differential inclusions of the form −u′′(t)∈F(t,u(t)),a.e.t∈(0,1),$$\begin{equation*}\hskip7pc -u^{\prime \prime }(t)\in F(t,u(t)),\; \text{a.e.} \; t \in (0,1), \end{equation*}$$subject to various nonlocal...

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Published inMathematische Nachrichten Vol. 296; no. 1; pp. 152 - 163
Main Authors Cianciaruso, Filomena, Pietramala, Paolamaria
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.01.2023
Subjects
Boundary conditions
differential inclusion
fixed point index
Inclusions
integral inclusion
nonlocal boundary condition
positive solution
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Summary:We give a unified approach to study the existence of multiple positive solutions of nonlinear differential inclusions of the form −u′′(t)∈F(t,u(t)),a.e.t∈(0,1),$$\begin{equation*}\hskip7pc -u^{\prime \prime }(t)\in F(t,u(t)),\; \text{a.e.} \; t \in (0,1), \end{equation*}$$subject to various nonlocal boundary conditions. We study these problems via a perturbed integral inclusion of the form u(t)∈Bu(t)+∫01k(t,s)F(s,u(s))ds$ u(t)\in Bu(t) +\int _{0}^{1}k(t,s)F(s,u(s))\,ds$.
Bibliography:Solutions for a wide class of differential inclusions.
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content type line 14
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202100385