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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Nonlinear elliptic boundary value problems for equations with rapidly (or slowly) increasing coefficients


Author: Jean-Pierre Gossez
Journal: Trans. Amer. Math. Soc. 190 (1974), 163-205
MSC: Primary 35J65
MathSciNet review: 0342854
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Abstract: Variational boundary value problems for quasilinear elliptic systems in divergence form are studied in the case where the nonlinearities are nonpolynomial. Monotonicity methods are used to derive several existence theorems which generalize the basic results of Browder and Leray-Lions. Some features of the mappings of monotone type which arise here are that they act in nonreflexive Banach spaces, that they are unbounded and not everywhere defined, and that their inverse is also unbounded and not everywhere defined.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0342854-2
Keywords: Quasilinear elliptic systems, nonpolynomial nonlinearities, existence theorems, nonlinear monotone mappings, nonlinear pseudomonotone mappings, Orlicz-Sobolev spaces, nonreflexive Banach spaces, complementary systems, noncoercive problems, local a priori bound
Article copyright: © Copyright 1974 American Mathematical Society