Multiple Solutions of Neumann Problems: An Orlicz–Sobolev Space Setting

Afrouzi, G. A.; Rădulescu, Vicenţiu D.; Shokooh, Saeid

doi:10.1007/s40840-015-0153-x

Cited by 9 publications

(3 citation statements)

References 33 publications

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“…Our analysis is based on the following theorems. These tools have been successfully applied to different problems in [2,4,9,13,17]. [14]).…”

Section: Preliminariesmentioning

confidence: 99%

Three solutions for a nonlinear equation involving p-triharmonic operators

2021

J. Nonlinear Funct. Anal.

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The existence of at least three weak solutions for a nonlinear elliptic Navier boundary value problem involving the p-triharmonic operator is investigated. The main tools used for obtaining our results are two critical points theorems established in [B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 9 (2009), 3084-3089] and [G. Bonanno, S.A. Marano, On the structure of the critical set of non-differentiable functionals with a weak compactness condition, Appl. Anal. 89 (2010), 1-10].

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“…Our analysis is based on the following theorems. These tools have been successfully applied to different problems in [2,4,9,13,17]. [14]).…”

Section: Preliminariesmentioning

confidence: 99%

Three solutions for a nonlinear equation involving p-triharmonic operators

2021

J. Nonlinear Funct. Anal.

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“…Many properties of Orlicz-Sobolev spaces and fractional Orlicz-Sobolev spaces come in [1,6,20,24,32]. For this, many researchers have studied the existence of solutions for the eigenvalue problems involving nonhomogeneous operators in the divergence form through Orlicz-Sobolev spaces by using variational methods and critical point theory, monotone operator methods, fixed point theory and degree theory (see for instance [2,3,4,7,8,9,10,11,14,28,29]).…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for a nonlocal type problem in fractional Orlicz Sobolev spaces

2020

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In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend the fractional Sobolev spaces W s,p to include the general case W s L A , where A is an N-function and s ∈ (0, 1). We are concerned with some qualitative properties of the space W s L A (completeness, reflexivity and separability). Moreover, we prove a continuous and compact embedding theorem of these spaces into Lebesgue spaces.

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“…They play a significant role in many fields of mathematics, such as approximation theory, partial differential equations, calculus of variations, nonlinear potential theory, the theory of quasi-conformal mappings, non-Newtonian fluids, image processing, differential geometry, geometric function theory and probability theory. Due to these, several authors have widely studied the existence of solutions for the eigenvalue problems involving non-homogeneous operators in the divergence form by means of variational methods and critical point theory, monotone operator methods, fixed point theory and degree theory, see for instance [2], [3], [4], [8], [6], [7], [9], [12], [16], [18], [19], [22], [25], [26], [28]. DOI 10.14712/1213DOI 10.14712/ -7243.2019 In this paper, we will study problem (1.1) in the Orlicz-Sobolev space.…”

Section: Introductionmentioning

confidence: 99%