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Ko, Bong-Soo,Lee, Yong-Hoon Korean Mathematical Society 2002 대한수학회지 Vol.39 No.3
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.
Existence and long-time behavior of solutions to Navier-Stokes-Voigt equations with infinite delay
Cung The Anh,Dang Thi Phuong Thanh 대한수학회 2018 대한수학회보 Vol.55 No.2
In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.
EXISTENCE AND LONG-TIME BEHAVIOR OF SOLUTIONS TO NAVIER-STOKES-VOIGT EQUATIONS WITH INFINITE DELAY
Anh, Cung The,Thanh, Dang Thi Phuong Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.
CHALISHAJAR, DIMPLEKUMAR,RAMKUMAR, K.,ANGURAJ, A. The Korean Society for Computational and Applied M 2022 Journal of applied and pure mathematics Vol.4 No.1/2
The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.
Ha, T.G.,Kim, D.,Jung, I.H. Pergamon Press ; Elsevier Science Ltd 2014 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.67 No.3
In this paper, we consider a semi-linear wave equation with damping and source terms. Using a potential well method, we prove the existence and uniqueness of global solutions of the wave equation and investigate uniform decay rates of solutions. Moreover, an example is given to illustrate our results.
Ha, Tae Gab Korean Mathematical Society 2017 대한수학회지 Vol.54 No.4
In this paper, we consider coupled wave equation of Kirchhoff type in a noncylindrical domain. This work is devoted to prove the existence and uniqueness of global solutions and decay for the energy of solutions.
Existence and iteration of monotone positive solutions for third-order three-point BVPs
Jian-Ping Sun,Ke Cao,Ya-Hong Zhao,Xian-Qiang Wang 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.1
This paper is concerned with the existence of monotone positive solutions for a class of nonlinear third-order three-point boundary value problem. By applying iterative techniques, we not only obtain the existence of monotone positive solutions, but also establish iterative schemes for approximating the solutions. An example is also included to illustrate the importance of the results obtained.
The existence result of certain singular boundary value problem
Kim, Kyoung-Hee,Lee, Yong-Hoon Korean Mathematical Society 1995 대한수학회논문집 Vol.10 No.3
We prove the existence of solution for a Dirichlet singular boundary value problem. The proofs are based on the method of upper and lower solutions.
Dimplekumar Chalishajar,K. Ramkumar,A. Anguraj 한국전산응용수학회 2022 Journal of Applied and Pure Mathematics Vol.4 No.1
The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter \mathtt{H}\in (\frac{1}{2}, 1). We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.
EXISTENCE AND ITERATION OF MONOTONE POSITIVE SOLUTIONS FOR THIRD-ORDER THREE-POINT BVPS
Sun, Jian-Ping,Cao, Ke,Zhao, Ya-Hong,Wang, Xian-Qiang The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.1
This paper is concerned with the existence of monotone positive solutions for a class of nonlinear third-order three-point boundary value problem. By applying iterative techniques, we not only obtain the existence of monotone positive solutions, but also establish iterative schemes for approximating the solutions. An example is also included to illustrate the importance of the results obtained.