• Title, Summary, Keyword: upper solutions

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Upper and lower solutions for a singular p-Laplacian system

  • Kim, Chan-Gyun;Lee, Eun-Kyoung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.4
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    • pp.89-99
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    • 2007
  • In this paper, we define the upper and lower solutions for a p-Laplacian system with singular nonlinearity at the boundaries. And we prove the theorem for the upper and power solutions method.

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THE METHOD OF LOWER AND UPPER SOLUTIONS FOR IMPULSIVE FRACTIONAL EVOLUTION EQUATIONS IN BANACH SPACES

  • Gou, Haide;Li, Yongxiang
    • Journal of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.61-88
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    • 2020
  • In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

EXISTENCE OF SOLUTIONS FOR BOUNDARY BLOW-UP QUASILINEAR ELLIPTIC SYSTEMS

  • Miao, Qing;Yang, Zuodong
    • Journal of applied mathematics & informatics
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    • v.28 no.3_4
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    • pp.625-637
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    • 2010
  • In this paper, we are concerned with the quasilinear elliptic systems with boundary blow-up conditions in a smooth bounded domain. Using the method of lower and upper solutions, we prove the sufficient conditions for the existence of the positive solution. Our main results are new and extend the results in [Mingxin Wang, Lei Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Analysis(In Press)].

TRAVELING WAVES OF AN SIRS EPIDEMIC MODEL WITH SPATIAL DIFFUSION AND TIME DELAY

  • Du, Yanke;Xu, Rui
    • Journal of applied mathematics & informatics
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    • v.30 no.3_4
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    • pp.635-646
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    • 2012
  • This paper is concerned with an SIRS epidemic model with spatial diffusion and time delay representing the length of the immunity period. By using a new cross iteration scheme and Schauder's fixed point theorem, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a newfashioned pair of upper-lower solutions, we derive the existence of a traveling wave solution connecting the uninfected steady state and the infected steady state.

THREE-POINT BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

  • Khan, Rahmat Ali
    • Journal of applied mathematics & informatics
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    • v.31 no.1_2
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    • pp.221-228
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    • 2013
  • The method of upper and lower solutions and the generalized quasilinearization technique is developed for the existence and approximation of solutions to boundary value problems for higher order fractional differential equations of the type $^c\mathcal{D}^qu(t)+f(t,u(t))=0$, $t{\in}(0,1),q{\in}(n-1,n],n{\geq}2$ $u^{\prime}(0)=0,u^{\prime\prime}(0)=0,{\ldots},u^{n-1}(0)=0,u(1)={\xi}u({\eta})$, where ${\xi},{\eta}{\in}(0,1)$, the nonlinear function f is assumed to be continuous and $^c\mathcal{D}^q$ is the fractional derivative in the sense of Caputo. Existence of solution is established via the upper and lower solutions method and approximation of solutions uses the generalized quasilinearization technique.

MULTIPLE SOLUTIONS IN NATURAL CONVECTION BETWEEN TWO HORIZONTAL PLATES WITH SMALL MAGNITUDE NON-UNIFORM TEMPERATURE IN THE UPPER PLATE (위 평판이 작은 불균일 온도를 갖는 두 수평 평판 사이의 자연 대류에서의 다중해)

  • Yoo, Joo-Sik
    • Journal of computational fluids engineering
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    • v.21 no.3
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    • pp.64-70
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    • 2016
  • Multiple solutions in natural convection of water with Pr=7 between two horizontal plates with small magnitude non-uniform temperature distribution in the upper plate is numerically investigated. The dimensionless temperature of upper plate is ${\theta}={\epsilon}sinkx$. Two upright cells are formed over one wave length in the conduction-dominated regime of small Rayleigh number. However, multicellular convection occurs above a critical Rayleigh number for small wave number. When k = 1.5, dual solutions are found and a transition of $6{\rightarrow}4$ eddy flow occurs with decrease of Rayleigh number. When k = 0.75, two, three, four and five multiple solutions are observed. Transitions of $14{\rightarrow}12$, $12{\rightarrow}10$, $10{\rightarrow}8$ and $6{\rightarrow}8$ eddy flow occur with decrease of Rayleigh number.