• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.763-772
• /
• 2010

This paper deals with the existence of triple positive solutions for the nonlinear second-order three-point boundary value problem z"(t)+a(t)f(t, z(t), z'(t))=0, t $\in$ (0, 1), $z(0)={\nu}z(1)\;{\geq}\;0$, $z'(\eta)=0$, where 0 < $\nu$ < 1, 0 < $\eta$ < 1 are constants. f : [0, 1] $\times$ [0, $+{\infty}$) $\times$ R $\rightarrow$ [0, $+{\infty}$) and a : (0, 1) $\rightarrow$ [0, $+{\infty}$) are continuous. First, Green's function for the associated linear boundary value problem is constructed, and then, by means of a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of triple positive solutions to the boundary value problem. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.895-902
• /
• 2009

In this paper, the singular three-point boundary value problem $$\{{{u"(t)\;+\;f(t,\;u)\;=\;0,\;t\;{\in}\;(0,\;1),}\atop{u(0)\;=\;0,\;u(1)\;=\;{\alpha}u(\eta),}}\$$ is studied, where 0 < $\eta$ < 1, $\alpha$ > 0, f(t,u) may be singular at u = 0. By mixed monotone method, the existence and uniqueness are established for the above singular three-point boundary value problems. The theorems obtained are very general and complement previous know results.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.3
• /
• pp.601-612
• /
• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Journal of Agricultural Extension & Community Development
• /
• v.17 no.4
• /
• pp.897-918
• /
• 2010

This paper researches conservative value evaluation of rural tourism villages with "CVM(Contingent Valuation Method)" focusing on visitor to offer the guide for preservation and management in landscape of rural tourism villages based on critical consciousness for conservation and utilization by regional development. The option value is 37,624won(36.7%), the bequest value is 34,856won(34.0%), existence value is 30,073 won(29.3%), and overall average willingness to pay of conservation value is 102,517won(100.0%) for conservative value of sesim-village in Kyung-Ju. The results show that landscape of rural tourism villages has great value historically and culturally. In conclusion, it suggested that planners and staffs of rural tourism villages recognize that it is positively necessary to be considered not only multiple landscape index but also conservation policy in process of development planning in rural tourism villages.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.275-283
• /
• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.103-112
• /
• 2009

We show the existence of the solutions for the following nonlinear elliptic problem under the Dirichlet boundary condition. To show the existence of the solutions we use the variational formulation.

• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.651-660
• /
• 2018

This paper concerned the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. By using Krasnoselskii fixed point theorem, we prove the existence of positive solutions according to the parameters under the proper nonlinear growth conditions.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.749-757
• /
• 2015

In this paper, we prove existence of radial positive solutions for the following boundary value problem

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.189-205
• /
• 2003

In this paper we prove the existence of solution and uniform decay rates of the energy to viscoelastic problems with nonlinear boundary damping term. To obtain the existence of solutions, we use Faedo-Galerkin's approximation, and also to show the uniform stabilization we use the perturbed energy method.

• East Asian mathematical journal
• /
• v.39 no.1
• /
• pp.43-50
• /
• 2023

This paper is concerned with the existence of positive solutions to the second order differential systems with strongly coupled integral boundary value conditions. The fixed point index theorems are used for the main results.