Advances in Differential Equations

Boundary-value problems for strongly nonlinear multivalued equations involving different $\Phi$-Laplacians

Laura Ferracuti and Francesca Papalini

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Abstract

We investigate the existence of solutions to the scalar differential inclusion $$ \qquad (D(x(t))\Phi(x'(t)))' \in G(t,x(t),x'(t)) \ \ \mbox{a.e. } t\in I=[0,T], $$ where $D(x)$ is a positive and continuous function, $G(t,x,x')$ is a Carathéodory multifunction and the increasing homeomorphism $\Phi$ can have a bounded domain of the type $(-a,a)$ or it can be the p-Laplacian operator. Using fixed-point techniques combined, in some cases, with the method of lower and upper solutions, we prove the existence of solutions satisfying various boundary conditions.

Article information

Source
Adv. Differential Equations Volume 14, Number 5/6 (2009), 541-566.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867259

Mathematical Reviews number (MathSciNet)
MR2502704

Zentralblatt MATH identifier
1179.34011

Subjects
Primary: 34B15: Nonlinear boundary value problems 34A60: Differential inclusions [See also 49J21, 49K21] 34C25: Periodic solutions

Citation

Ferracuti, Laura; Papalini, Francesca. Boundary-value problems for strongly nonlinear multivalued equations involving different $\Phi$-Laplacians. Adv. Differential Equations 14 (2009), no. 5/6, 541--566. https://projecteuclid.org/euclid.ade/1355867259.


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