Mountain pass type solutions for quasilinear elliptic inclusions
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Date
2002
Journal Title
Journal ISSN
Volume Title
Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
Abstract
We establish the existence of weak solutions to the inclusion problem
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where Omega is a bounded domain in R-N, g is an element of C((&UOmega;) over bar x R, R), and psi is an element of R x R is a maximal monotone odd graph. Under suitable conditions on psi, g (which reduce to subcritical and superlinear conditions in the case of powers) we obtain the existence of non-trivial solutions which are of mountain pass type in an appropriate not necessarily reflexive Orlicz Sobolev space. The proof is based on a version of the Mountain Pass Theorem for a non-smooth case.
[GRAPHICS]
where Omega is a bounded domain in R-N, g is an element of C((&UOmega;) over bar x R, R), and psi is an element of R x R is a maximal monotone odd graph. Under suitable conditions on psi, g (which reduce to subcritical and superlinear conditions in the case of powers) we obtain the existence of non-trivial solutions which are of mountain pass type in an appropriate not necessarily reflexive Orlicz Sobolev space. The proof is based on a version of the Mountain Pass Theorem for a non-smooth case.
Description
Keywords
Mountain Pass Lemma, Orlicz-Sobolev spaces, generalized gradient, subdifferential, quasilinear elliptic, BOUNDARY-VALUE PROBLEMS, EQUATIONS