2020
DOI: 10.3390/axioms9030109
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The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

Abstract: The purpose of this work is to prove the existence and uniqueness of a class of nonlinear unilateral elliptic problem (P) in an arbitrary domain, managed by a low-order term and non-polynomial growth described by an N-uplet of N-function satisfying the Δ2-condition. The source term is merely integrable.

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Cited by 17 publications
(16 citation statements)
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“…In particular, using the theory of pseudomonotone operators, Gasiński, and Winkert in [16] proved the existence and uniqueness of a weak solution to quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient, under quite general assumptions on the convection term and towering some linear conditions on the gradient variable. Finally, for a deeper comprehension, we refer the reader to [1,3,[5][6][7][8][9]11] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…In particular, using the theory of pseudomonotone operators, Gasiński, and Winkert in [16] proved the existence and uniqueness of a weak solution to quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient, under quite general assumptions on the convection term and towering some linear conditions on the gradient variable. Finally, for a deeper comprehension, we refer the reader to [1,3,[5][6][7][8][9]11] and the references therein.…”
Section: Introductionmentioning
confidence: 99%
“…We start by a pioneer work published by Liu and Li in [25] for multiplicity results with superlinear nonlinearities, using the critical point theory with Cerami condition which is weaker than the Palais-Smale condition. For a deeper comprehension, we recommend that readers consult [3,4,6,8,9,10,11] and the references therein. In Sobolev space with variable exponent, some other useful contributions have been devoted to the study but first of all the experts in the field immediately think, among all, to the study made by Colombo and Mingione in [16] and Baroni, Colombo, and Mingione [7].…”
Section: Introductionmentioning
confidence: 99%
“…Also, there are many articles on nonstandard growth problems, especially on p(x)-growth and double phase problems. About p(x)-growth problems, see [1,2,4,5,6,7,8,9,11,12,22] and the references given there.…”
Section: Introductionmentioning
confidence: 99%