• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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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.

• 대한수학회지
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• 제57권1호
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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.

• 대한수학회지
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• 제43권6호
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• pp.1253-1268
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• 2006

We develop the upper and lower solutions method for the four point problem relative to second order differential equations in order to obtain the existence of solution.

• 대한수학회지
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• 제51권6호
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• pp.1123-1139
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• 2014

In this work, we investigate the existence of the extremal solutions for a class of fractional partial differential equations with order 1 < ${\alpha}$ < 2 by upper and lower solution method. Using the theory of Hausdorff measure of noncompactness, a series of results about the solutions to such differential equations is obtained.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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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.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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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)].

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.553-558
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• 2008

The method of upper and lower solutions coupled with monotone iterative technique is used to obtain the results of existence and uniqueness for an anti-periodic boundary value problem of impulsive differential equations with delay.

• 대한수학회지
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• 제39권3호
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.

• 대한수학회지
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• 제45권6호
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• pp.1549-1559
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• 2008

In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1361-1370
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• 2009

In this paper, we consider singular fourth-order two point boundary value problems $u^{(4)}$ (t) = f(t, u), 0 < t < 1, u(0) = u(l) = u'(0) = u'(l) = 0, where $f:(0,1){\times}(0,+{\infty}){\rightarrow}[0,+{\infty})$ may be singular at t = 0, 1 and u = 0. By using the upper and lower solution method, we obtained the existence of positive solutions to the above boundary value problems. An example is also given to illustrate the obtained theorems.