Radial solutions of a nonlinear k-Hessian system involving a nonlinear operator

Wang, Guotao; Yang, Zedong; Zhang, Lihong; Băleanu, Dumitru

doi:10.1016/j.cnsns.2020.105396

Cited by 38 publications

(17 citation statements)

References 32 publications

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“…One of the important definition which has very recently attracted the attention is the

derivative introduced by Atangana-Baleanu and Caputo [38] in 2016. The fractal-fractional derivatives exhibit the singular kernel by nonsingular kernel and therefore were greatly studied in [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [56] , [57] , [58] , [59] . Now the question how to solve these problems.…”

Section: Introductionmentioning

confidence: 99%

A comparative study of spreading of novel corona virus disease by ussing fractional order modified SEIR model

Alrabaiah¹,

Arfan²,

Shah³

et al. 2021

Alexandria Engineering Journal

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In this research work, a non-linear dynamical modified SEIR model of the recent pandemic, due to Coronavirus-19 disease (COVID-19) for different countries like Malaysia and Pakistan, is considered under nonsingular fractional order derivative. For this model, some qualitative results, existence theory, and numerical solution are studied by using fixed point approach and fractional Adams-Bashforth method. The results are simulated corresponding to some real data of various fractional order by using Matlab. Hence, the suitability of the considered COVID-19 model for the current outbreak in two different countries Malaysia and Pakistan are shown by simulation.

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“…One of the important definition which has very recently attracted the attention is the

Section: Introductionmentioning

confidence: 99%

A comparative study of spreading of novel corona virus disease by ussing fractional order modified SEIR model

Alrabaiah¹,

Arfan²,

Shah³

et al. 2021

Alexandria Engineering Journal

View full text Add to dashboard Cite

show abstract

“…Also, we develop the monotone iterative technique for the system. e advantage of the technique needs no special emphasis [33][34][35][36][37][38][39][40]. It is worth to point that, in this paper, only half pair of upper and lower solutions is assumed to the system, which is weaker than a pair of upper and lower solutions.…”

Section: Introductionmentioning

confidence: 99%

Monotone Iterative Method for Two Types of Integral Boundary Value Problems of a Nonlinear Fractional Differential System with Deviating Arguments

Chen

Qin²

2021

Journal of Mathematics

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This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, i . e ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.

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“…In this paper, we shall establish the existence and multiplicity of nontrivial radial k-admissible solutions of the weakly coupled degenerated system (1.1). It is worth to notice that the system (1.1) contains a variety of different k-Hessian equations which is significantly different from that in [5,7,23,29] such that the problem we considered can contain Laplace equations and Monge-Ampère equations at the same time. This kind of system can represent the coupling of different types of elliptic equations, which makes our problem more comprehensive and more applicable.…”

Section: Introductionmentioning

confidence: 99%

On the solutions to weakly coupled system of $\boldsymbol{k_i}$-Hessian equations

Ji¹,

Jiang²,

Dong³

2021

Preprint

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In this paper, the existence and multiplicity of nontrivial radial convex solutions to general coupled system of ki-Hessian equations in a unit ball are studied via a fixed-point theorem. In particular, we obtain the uniqueness of nontrivial radial convex solution and nonexistence of nontrivial radial kadmissible solution to a power-type system coupled by ki-Hessian equations in a unit ball. Moreover, using a generalized Krein-Rutman theorem, the existence of k-admissible solutions to an eigenvalue problem in a general strictly (k − 1)-convex domain is also obtained.

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Radial solutions of a nonlinear k-Hessian system involving a nonlinear operator

Cited by 38 publications

References 32 publications

A comparative study of spreading of novel corona virus disease by ussing fractional order modified SEIR model

A comparative study of spreading of novel corona virus disease by ussing fractional order modified SEIR model

Monotone Iterative Method for Two Types of Integral Boundary Value Problems of a Nonlinear Fractional Differential System with Deviating Arguments

On the solutions to weakly coupled system of $\boldsymbol{k_i}$-Hessian equations

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