The Existence and Uniqueness of an Entropy Solution to Unilateral Orlicz Anisotropic Equations in an Unbounded Domain

et al. 2022

Preprint

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The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for all small values of the parameter λ > 0, there exist at least two non-trivial positive solutions. Our results extend the previous works Papageorgiou, Repovš, and Vetro [24] and Liu, Dai, Papageorgiou, and Winkert [21], from the case of Musielak-Orlicz Sobolev space, when exponents p and q are constant, to the case of Sobolev-Orlicz spaces with variable exponents in a complete manifold.

Section: Introductionmentioning

confidence: 99%

Existence of solutions for a singular double phase in Sobolev-Orlicz spaces with variable exponents in a complete manifold

Aberqi¹,

Bennouna²,

et al. 2022

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“…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%

Weak solvability of nonlinear elliptic equations involving variable exponents

Aberqi¹,

Bennouna²,

et al. 2022

Preprint

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the (p(m), q(m))− equation and the nonlinearity is superlinear but does not fulfil the Ambrosetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a (p(m), q(m)) equation that highlights the applicability of our theoretical results is also provided.

“…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%

Existence Results for double phase problem in Sobolev-Orlicz spaces with variable exponents in Complete Manifold

Aberqi¹,

Bennouna²,

et al. 2021

Preprint

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In this paper, we study the existence of non-negative non-trivial solutions for a class of double-phase problems where the source term is a Caratheodory function that satisfies the Ambrosetti-Rabinowitz type condition in the framework of Sobolev-Orlicz spaces with variable exponents in complete compact Riemannian n-manifolds. Our approach is based on the Nehari manifold and some variational techniques. Further-more, the Hölder inequality, continuous and compact embedding results are proved.