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May/June 2009 Boundary-value problems for strongly nonlinear multivalued equations involving different $\Phi$-Laplacians
Laura Ferracuti, Francesca Papalini
Adv. Differential Equations 14(5/6): 541-566 (May/June 2009).

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.

Citation

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Laura Ferracuti. Francesca Papalini. "Boundary-value problems for strongly nonlinear multivalued equations involving different $\Phi$-Laplacians." Adv. Differential Equations 14 (5/6) 541 - 566, May/June 2009.

Information

Published: May/June 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1179.34011
MathSciNet: MR2502704

Subjects:
Primary: 34A60, 34B15, 34C25

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.14 • No. 5/6 • May/June 2009
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