• Korean Journal of Mathematics
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• 제26권1호
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• pp.9-21
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• 2018

We investigate existence and multiplicity of the solutions for elliptic boundary value problem with two singularities. We obtain one theorem which shows that there exists at least one nontrivial weak solution under some conditions on which the corresponding functional of the problem satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.

• East Asian mathematical journal
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• 제29권3호
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• pp.303-314
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• 2013

In this paper, we introduce an iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a finite family of asymptotically ${\kappa}$-strict pseudo-contractions in Hilbert spaces. Weak and strong convergence theorems are established for the iterative scheme.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.147-163
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• 2017

In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).

• Korean Journal of Mathematics
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• 제21권4호
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• pp.483-493
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• 2013

We investigate the multiplicity of the solutions for a class of the system of the biharmonic equations with some singular potential nonlinearity. We obtain a theorem which shows the existence of the nontrivial weak solution for a class of the system of the biharmonic equations with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and the generalized mountain pass theorem.

• 대한수학회지
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• 제51권6호
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• 대한수학회지
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• 제38권2호
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• pp.321-336
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• 2001

A Feynman functional formulation is given for the Global Positioning System, GPS. Both the sequential and analytic Feynman functionals are presented for the classical, exterior, gravity problems which included rigid body rotations, special relativity and some general relativity corrections. A mathematically rigorous approach is introduced whose solutions exist, are unique and which depend continuously on the intial data. This formulation is convergent and has the finite approximation property. It is emphasized that all of the problems studied are classical (not quantum) evolution systems.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.145-161
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• 2020

In this article, we study the solvability of the Cauchy-Dirichlet problem for a class of nonlinear parabolic equations with nonstandard growth and nonlocal terms. We prove the existence of weak solutions of the considered problem under more general conditions. In addition, we investigate the behavior of the solution when the problem is homogeneous.

• 대한수학회논문집
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• 제21권2호
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• pp.273-285
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• 2006

In this paper, we shall give an affirmative answer to the question raised by Kim and Tan [1] dealing with generalized vector quasi-variational inequalities which generalize many existence results on (VVI) and (GVQVI) in the literature. Using the maximal element theorem, we derive two theorems on the existence of weak solutions of (GVQVI), one theorem on the existence of strong solution of (GVQVI), and one theorem on strong solution in the 1-dimensional case.

• 대한수학회논문집
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• 제28권4호
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• pp.751-766
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• 2013

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

• 충청수학회지
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• 제34권1호
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• pp.85-92
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• 2021

In present paper, inspired by the recently paper [1], we give the mixed pressure-velocity regular criteria in view of Lorentz spaces for weak solutions to 3D micropolar equations in a half space. Precisely, if (0.1) ${\frac{P}{(e^{-{\mid}x{\mid}^2}+{\mid}u{\mid})^{\theta}}{\in}L^p(0,T;L^{q,{\infty}}({\mathbb{R}}^3_+))$, p, q < ∞, and (0.2) ${\frac{2}{p}}+{\frac{3}{q}}=2-{\theta}$, 0 ≤ θ ≤ 1, then (u, w) is regular on (0, T].