• East Asian mathematical journal
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• v.26 no.5
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• pp.681-691
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• 2010

A system of variational inclusions with (A, ${\eta}$, m)-accretive operators in real q-uniformly smooth Banach spaces is introduced. Using the resolvent operator technique associated with (A, ${\eta}$, m)-accretive operators, we prove the existence and uniqueness of solutions for this system of variational inclusions and propose a Mann type iterative algorithm for approximating the unique solution for the system of variational inclusions.

• East Asian mathematical journal
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• v.26 no.5
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• pp.703-714
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• 2010

A new class of nonlinear set-valued mixed variational inclusions involving (A, ${\eta}$)-accretive mappings in Banach spaces is introduced and studied, which includes many kind of variational inclusion (inequality) and complementarity problems as special cases. By using the resolvent operator associated with (A, ${\eta}$)-accretive operator due to Lan-Cho-Verma, the existence of solution for this kind of variational inclusion is proved, and a new hybrid proximal point algorithm is established and suggested, the convergence and stability theorems of iterative sequences generated by new iterative algorithms are also given in q-uniformly smooth Banach spaces.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.57-71
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• 2013

In this paper, we establish the existence of at least three solutions to a Navier boundary problem involving the ($p_1$, ${\cdots}$, $p_n$)-biharmonic systems. We use a variational approach based on a three critical points theorem due to Ricceri [B. Ricceri, A three critical points theorem revisited, Nonlinear Anal. 70 (2009), 3084-3089].

• Korean Journal of Mathematics
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• v.22 no.2
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• pp.355-365
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• 2014

We show the existence of nontrivial solutions for some fourth order elliptic boundary value problem with fully nonlinear term. We obtain this result by approaching the variational method and using a linking theorem. We also get a uniqueness result.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Bulletin of the Korean Mathematical Society
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• v.53 no.6
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• pp.1753-1769
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• 2016

This paper is concerned with the quasilinear $Schr{\ddot{o}}dinger$ system $$(0.1)\;\{-{\Delta}u+a(x)u-{\Delta}(u^2)u=Fu(u,v)+h(x)\;x{\in}{\mathbb{R}}^N,\\-{\Delta}v+b(x)v-{\Delta}(v^2)v=Fv(u,v)+g(x)\;x{\in}{\mathbb{R}}^N,$$ where $N{\geq}3$. The potential functions $a(x),b(x){\in}L^{\infty}({\mathbb{R}}^N)$ are bounded in ${\mathbb{R}}^N$. By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (0.1).

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1551-1571
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• 2020

This paper is concerned with the following Kirchhoff-Schrödinger-Poisson system $$\begin{cases} -(a+b{\displaystyle\smashmargin{2}\int\nolimits_{\mathbb{R}^3}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+{\mu}{\phi}u={\lambda}f(x){\mid}u{\mid}^{p-2}u+g(x){\mid}u{\mid}^{p-2}u,&{\text{ in }}{\mathbb{R}}^3,\\-{\Delta}{\phi}={\mu}{\mid}u{\mid}^2,&{\text{ in }}{\mathbb{R}}^3, \end{cases}$$ where a > 0, b, µ ≥ 0, p ∈ (1, 2), q ∈ [4, 6) and λ > 0 is a parameter. Under some suitable assumptions on V (x), f(x) and g(x), we prove that the above system has at least two different nontrivial solutions via the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Some recent results from the literature are improved and extended.

• Smart Structures and Systems
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• v.13 no.1
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• pp.111-135
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• 2014

Based on the Reissner mixed variational theorem (RMVT), finite rectangular layer methods (FRLMs) are developed for the three-dimensional (3D) linear buckling analysis of simply-supported, fiber-reinforced composite material (FRCM) and functionally graded material (FGM) sandwich plates subjected to bi-axial compressive loads. In this work, the material properties of the FGM layers are assumed to obey the power-law distributions of the volume fractions of the constituents through the thickness, and the plate is divided into a number of finite rectangular layers, in which the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-plane variations of the field variables of each individual layer, respectively, and an h-refinement process is adopted to yield the convergent solutions. The accuracy and convergence of the RMVT-based FRLMs with various orders used for expansions of each field variables through the thickness are assessed by comparing their solutions with the exact 3D and accurate two-dimensional ones available in the literature.

• Structural Engineering and Mechanics
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• v.27 no.4
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• pp.457-475
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• 2007

Analysis of transverse stresses at layer interfaces in a composite laminate has always been a challenging task. Composite structures possess highly irregular material properties at layer interfaces, which cause high shear stresses. Classical Plate Theory and First Order Shear Deformation Theory (FSDT) use post computing to calculate transverse stresses. This paper presents Reissner Mixed Variational Theorem (RMVT) based finite element model to carry out layer-wise analysis of composite laminates. Selective integration scheme has been used. The formulation has been validated by solving numerical examples and comparing the results with those published in the literature.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.423-436
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• 2011

We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.