• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1213-1222
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• 2012

The aim of this paper is to establish the existence of three solutions for a Sturm-Liouville mixed boundary value problem. The approach is based on multiple critical points theorems.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.125-144
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• 2017

Three nontrivial nonnegative solutions for some critical quasilinear elliptic systems with lower-order negative perturbations are obtained by using the Ekeland's variational principle and the mountain pass theorem.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.187-220
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• 2016

This paper is concerned with a kind of non-homogeneous boundary value problems for singular second order differential systems with Laplacian operators. Using multiple fixed point theorems, sufficient conditions to guarantee the existence of at least three solutions of this kind of boundary value problems are established. An example is presented to illustrate the main results.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.407-414
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• 2020

In this article, a second-order Sturm-Liouville problem with impulsive effects and involving the one-dimensional p-Laplacian is considered. The existence of at least three weak solutions via variational methods and critical point theory is obtained.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.531-551
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• 2021

In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.3
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• pp.11-18
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• 2001

A simple and convenient method of analysis for obtaining the individual stress intensity factors in a three-dimensional mixed mode crack is proposed. The procedures presented here are based on the path independence of J integral and mutual or two-state conservation integral, which involves two elastic fields. The problem is reduced to the determination of mixed mode stress intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. Some numerical examples are presented to investigate the effectiveness and applicability of the method for a three-dimensional penny-shaped crack problem under mixed mode. This procedure is applicable to a three-dimensional mixed mode curved crack.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.507-515
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• 2012

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

• Journal of the Korean Applied Science and Technology
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• v.26 no.1
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• pp.45-50
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• 2009

Three-dimensional, statistical-mechanical formulations of problems are usually untractable analytically, and therefore they are commonly solved numerically. However, their one-dimensional counterparts are always to be solved analytically. In general analytical solutions sheds more insights to the problems than numerical solutions. Hence, solutions of one-dimensional problems may provide key properties to the problems, when they are extended to three dimensions. In this article, thermodynamic properties of one-dimensional fluid comprising molecules of rigid rods are analyzed statistical-mechanically. Molecules of rigid rods are characterized with repulsive or excluded volume effect. It is observed that this feature is well reflected in thermodynamic functions such as Helmholtz free energy. volumetric equation of state. chemical potential, entropy, etc.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1813-1817
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• 2007

The present work presents plastic limit load solutions for piping branch junctions with local wall-thinning, based on detailed three-dimensional (3-D) and small strain FE limit analyses using elastic-perfectly plastic materials. Three types of loading are considered; internal pressure, in-plane bending on the branch pipe and in-plane bending on the run pipe. The wall-tinning located on variable area of the piping branch junction is considered. A wide range of piping branch junction and wall-thinning geometries are considered. Comparison of the proposed solutions with FE results shows good agreement

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.329-338
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• 2014

In this paper, we study the method of upper and lower solutions and develop the generalized quasilinearization technique for the existence and approximation of solutions to some three-point nonlocal boundary value problems associated with higher order fractional differential equations of the type $$^c{\mathcal{D}}^q_{0+}u(t)+f(t,u(t))=0,\;t{\in}(0,1)$$ $$u^{\prime}(0)={\gamma}u^{\prime}({\eta}),\;u^{\prime\prime}(0)=0,\;u^{\prime\prime\prime}(0)=0,{\ldots},u^{(n-1)}(0)=0,\;u(1)={\delta}u({\eta})$$, where, n-1 < q < n, $n({\geq}3){\in}\mathbb{N}$, 0 < ${\eta},{\gamma},{\delta}$ < 1 and $^c\mathcal{D}^q_{0+}$ is the Caputo fractional derivative of order q. The nonlinear function f is assumed to be continuous.