Existence of multiple solutions for second-order discrete boundary value problems

Henderson, Johnny; Thompson, H. B.

doi:10.1016/s0898-1221(02)00095-0

Cited by 114 publications

(57 citation statements)

References 4 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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“…Then Gupta [5] studied three-point boundary value problems for nonlinear second order ordinary differential equations. Since then, the existence of positive solutions for nonlinear second-order three point boundary value problems have also been studied by many authors by using the fixed point theorems or coincidence degree theory, one may see the text books [1,2] and the papers [3][4][5][6][7][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we are interested in the analysis of qualitative theory of the problems of the existence of positive solutions to second-order difference equations. Inspired and motivated by the works mentioned above and the papers [3][4][5][6][7][10][11][12][13][14][15][16][17] and the references therein, we concentrate on the existence of positive solutions for the following secondorder difference equation with three-point summation boundary value problem…”

Section: Introductionmentioning

confidence: 99%

Positive solutions for a second-order difference equation with summation boundary conditions

Bouchelaghem¹,

Ardjouni²,

Djoudi³

2017

Kragujevac J Math

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“…Important tools in the study of nonlinear difference equations are fixed point methods in cone; see [2,19], and upper and lower solution techniques; see, for instance, [24,25] and references therein. It is well known that critical point theory is an important tool to deal with the problems for differential equations.…”

Section: Introductionmentioning

confidence: 99%