Existence and nonexistence of positive solutions for the fractional coupled system involving generalized p-Laplacian

Wang, Ying; Jiang, Jiqiang

doi:10.1186/s13662-017-1385-x

Cited by 52 publications

(36 citation statements)

References 11 publications

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“…For a more complex situation, we refer the reader to [14]. The related studies on the elliptic equations also can be found in [15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

Han

Yao

2018

Advances in Mathematical Physics

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We study the existence and uniqueness of positive solution for the following -Laplacian-Kirchhoff-Schrödinger-type equation:where Ω ⊂ ( ≥ 3), , ≥ 0 are parameters, V( ), ( ), ( ) and ℎ are under some suitable assumptions. For the purpose of overcoming the difficulty caused by the appearance of the Schrödinger term and general singularity, we use the variational method and some mathematical skills to obtain the existence and uniqueness of the solution to this problem.

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“…For a more complex situation, we refer the reader to [14]. The related studies on the elliptic equations also can be found in [15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

Han

Yao

2018

Advances in Mathematical Physics

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“…The fractional calculus is regarded as an extension of ordinary differentiation and integration. [14][15][16][17][18][19][20][21][22] During the past several decades, fractional calculus has been remained slow development due to its complexity and the lack of real background. In the last several decades, the fractional calculus has been widely applied in numerous areas such as physics, mechanics, engineering, viscoelasticity, and biology.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis for a fractional‐order chemotherapy model with two different delays

Liao

et al. 2019

Math Methods in App Sciences

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Cancer is one of the most serious diseases in the world. The investigation on cancer treatment has attracted great attention from medical workers, mathematical researchers, and scholars in various fields. To understand the intrinsic characteristics of cancer, numerous scholars have established cancer treatment models and discussed the dynamical properties. However, the main work of many scholars only focuses on the integer-order cancer treatment models, while the study on fractional-order ones is quite a few. In the present article, on the basis of previous publications, we will put up a new fractional-order chemotherapy model with two different delays. By applying the stability theory and the Hopf bifurcation of fractional-order differential equations, we obtain a series of new stability criteria of the involved model and some sufficient conditions to ensure the existence of Hopf bifurcation of the involved model. Furthermore, the impact of two different delays and the fractional order on the stability and the emergence of Hopf bifurcation of involved model is presented.To illustrate the validity of analytical predictions, we perform computer simulations with Matlab software. The theoretical results in the manuscript are innovative and play an important role in cancer treatment.

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“…Fractional differential equations BVP has become a hot issue; see the monographs of Lakshmikantham and Vatsala [1], Rudin [2], Samko et al [3], Agarwal et al [4,5], and Webb and Zima [6]. Many excellent results have been reported; see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In [24], El-Sayed and Bin-Taher study the following m-point BVP:…”

Section: Introductionmentioning

confidence: 99%

Positive Solutions to n-Order Fractional Differential Equation with Parameter

Tan

Zhou

2018

Journal of Function Spaces

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By employing the properties of the sum operators, we investigate the solutions of the -order fractional differential equations multiple point boundary value problem (in short BVP) with the boundary conditions contains a parameter. We not only obtain the existence and uniqueness of solutions about this BVP but also construct an iterative scheme to approximate the solution which is important for practical application. An example is given to demonstrate the validity of our main results.

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Existence and nonexistence of positive solutions for the fractional coupled system involving generalized p-Laplacian

Cited by 52 publications

References 11 publications

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

Existence and Uniqueness of Positive Solution for p-Laplacian Kirchhoff-Schrödinger-Type Equation

Bifurcation analysis for a fractional‐order chemotherapy model with two different delays

Positive Solutions to n-Order Fractional Differential Equation with Parameter

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