Existence of three positive pseudo-symmetric solutions for a one dimensional p-Laplacian

Avery, Richard I.; Henderson, Johnny

doi:10.1016/s0022-247x(02)00308-6

Cited by 88 publications

(56 citation statements)

References 3 publications

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“…In this context, anisotropic discrete nonlinear problems involving p(k)-Laplacian operator seem to have attracted a great deal of attention due to its usefulness of modelling some more complicated phenomenon such us fluid dynamics and nonlinear elasticity. We refer the reader to [1,2,3,4,5,6,7,9,12,13,14,16,17,18,19,20,21,22,24] and references therein, where they could find the detailed background as well as many different approaches and techniques applied in the related area.…”

Section: Q(k)mentioning

confidence: 99%

Existence results to a nonlinear p(k)-Laplacian difference equation

Moghadam

Avcı

2017

Journal of Difference Equations and Applications

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Abstract. In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary condition is investigated. The main technical tools applied here are the two local minimum theorems for differentiable functionals given by Bonanno. IntroductionThe main goal of the present paper is to establish the existence of non-trivial solution for the following discrete anisotropic problem We want to remark that problem (1.1) is the discrete variant of the variable exponent anisotropic problem2) where Ω ⊂ R N , N ≥ 3 is a bounded domain with smooth boundary, f ∈ C(Ω×R, R) is given function that satisfy certain properties and p i (x), w i (x) ≥ 1 and q(x) ≥ 1 are continuous functions on Ω with 2 ≤ p i (x) for each x ∈ Ω and every i ∈ 2000 Mathematics Subject Classification. 39F20, 34B15.

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Section: Q(k)mentioning

confidence: 99%

Existence results to a nonlinear p(k)-Laplacian difference equation

Moghadam

Avcı

2017

Journal of Difference Equations and Applications

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“…As we know, some researchers [2,14] had discussed BVPs with at least three solutions. In these papers, the relative conclusions were based on the assumption that f (t, u(t)) be more than or less than a given constant.…”

Section: The Case Of No Less Than Three Solutionsmentioning

confidence: 99%

The boundary value problems of quadratic mixed type of delay differential equations with eigenvalues

Shen

2014

Mathematica Slovaca

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“…For the general background of difference equations, one can refer to monographs [1,21,25]. Since the last decade, there has been much progress on the qualitative properties of difference equations, which included results on stability and attractivity [13,23,39] and results on oscillation and other topics, see [1][2][3]5,10,[16][17][18][19]22,[34][35][36][37][38].…”

Section: R (T)u (T) = F (T U(t + 1) U(t) U(t − 1)) T ∈ Rmentioning

confidence: 99%