Existence of Solutions for a One Dimensional<i>p</i>-Laplacian on Time-Scales

Anderson, Douglas R.; Avery, Richard I.; Henderson, Johnny

doi:10.1080/10236190410001731416

Cited by 74 publications

(36 citation statements)

References 22 publications

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“…Meanwhile, the boundary value problems with p-Laplacian operator have also been discussed extensively in the literature, for example, see [3,7,9,16,22,23].…”

Section: Introductionmentioning

confidence: 99%

Multiple positive solutions for a fourth-order p-Laplacian Sturm-Liouville boundary value problems on time scales

Ding

Wei

2015

Acta Math. Appl. Sin. Engl. Ser.

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In this paper, we investigate the existence of multiple positive solutions for the following fourthorder p-Laplacian Sturm-Liouville boundary value problems on time scaleswhere φp(s) is the p-Laplacian operator. Under growth conditions on the nonlinearity f some existence results of at least two and three positive solutions for the above problem are obtained by virtue of fixed point theorems on cone. In particular, the nonlinearity f may be both sublinear and superlinear.

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“…Meanwhile, the boundary value problems with p-Laplacian operator have also been discussed extensively in the literature, for example, see [3,7,9,16,22,23].…”

Section: Introductionmentioning

confidence: 99%

Multiple positive solutions for a fourth-order p-Laplacian Sturm-Liouville boundary value problems on time scales

Ding

Wei

2015

Acta Math. Appl. Sin. Engl. Ser.

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“…In recent years, dynamic equations on time scales have found a considerable interest and attracted by many researchers; see, for example, [1][2][3][4][5][6][7][8][9][10][11]. The reason seems to be twofold.…”

Section: Introductionmentioning

confidence: 99%

Existence and Iteration of Positive Solutions to Third-Order BVP for a Class ofp-Laplacian Dynamic Equations on Time Scales

Rao¹

2015

International Journal of Differential Equations

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We investigate the existence and iteration of positive solutions for the following third-order -Laplacian dynamic equations on time scales: ( (( ) is -Laplacian operator; that is, ( ) = | | −2 , > 1, −1 = , and 1/ + 1/ = 1. By applying the monotone iterative technique and without the assumption of the existence of lower and upper solutions, we not only obtain the existence of positive solutions for the problem, but also establish iterative schemes for approximating the solutions.

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“…Problem (1.1), (1.2) is a generalization to time scales of the problem when T is restricted to R on the unit interval in Ma and Thompson [19], and extends the type of time-scale boundary value problem found in Anderson [2], Atici and Guseinov [6], Kaufmann [15], Kaufmann and Raffoul [16], and Sun and Li [21,22]. Other related three-point problems on time scales include Anderson and Avery [4], Anderson et al [5], Peterson et al [20], and a singular problem in DaCunha et al [12]. Some of the work on multipoint time-scale problems includes Anderson [1,3] and Kong and Kong [17], and a recent singular multipoint problem in Bohner and Luo [8].…”

Section: Introductionmentioning

confidence: 99%