• Korean Journal of Mathematics
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• 제19권4호
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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.

• Kyungpook Mathematical Journal
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• 제60권3호
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• pp.647-671
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• 2020

In this paper, we consider the Cauchy-type problem for a nonlinear differential equation involving a Ψ-Hilfer fractional derivative and prove the existence and uniqueness of solutions in the weighted space of functions. The Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the Cauchy-type problem is investigated via the successive approximation method. Further, we investigate the dependence of solutions on the initial conditions and their uniqueness using 𝜖-approximated solutions. Finally, we present examples to illustrate our main results.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.303-322
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• 2021

The concepts of new classes of mappings are introduced in the spaces which are more general space than the usual metric spaces. The existence and uniqueness of common fixed points and fixed point results are established in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a complete complex valued b-metric spaces.

• 대한수학회지
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• 제61권1호
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• pp.133-147
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• 2024

Let G = (V, E) be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on G $${\Delta}u={\lambda}e^u(e^u-1)^5+4{\pi}\sum_{s=1}^{N}\delta_{ps}$$, where λ > 0, δ_ps is the Dirac mass at the vertex p_s, and p₁, p₂, . . . , p_N are arbitrarily chosen distinct vertices on the graph. We show that there exists a critical value $\hat{\lambda}$ such that when λ > $\hat{\lambda}$, the generalized Chern-Simons equation has at least two solutions, when λ = $\hat{\lambda}$, the generalized Chern-Simons equation has a solution, and when λ < $\hat{\lambda}$, the generalized Chern-Simons equation has no solution.

• 호남수학학술지
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• 제30권2호
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• pp.259-272
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• 2008

We are concerned with the robust control problem for the chemotaxis equations with predator-prey dynamics. That is, we present the existence and uniqueness of the solution. We also show the existence of the robust control and deduce the corresponding optimality conditions.

• 대한수학회지
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• 제43권4호
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• pp.733-763
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• 2006

We study quasi-stationary Stokes flow in a dihedral domain arising from a study of a free boundary problem of viscous fluid in a container. We construct an exact solution of quasi-stationary Stokes equations and derive its estimates with norm in a weighted Sobolev spaces.

• 대한수학회보
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• 제47권2호
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• pp.355-367
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• 2010

In this paper, the existence of periodic solutions is obtained for a kind of p-Laplacian systems by the minimax methods in critical point theory. Moreover, the existence of infinite periodic solutions is also obtained.

• 대한수학회보
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• 제51권1호
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• pp.43-54
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• 2014

This paper is concerned with nonlinear evolution differential equations with infinite delay in Banach spaces. Using Kato's approximating approach, existence and uniqueness of strong solutions are obtained.

• East Asian mathematical journal
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• 제32권3호
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• pp.387-397
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• 2016

This paper is concerned with the optimal control problem for some reaction diusion model. That is, we show the existence of the global weak solution for the Field-Noyes model. We also show the existence of the optimal control.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.547-554
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• 2014

In this paper, we consider the existence and uniqueness of global weak solution for a sixth-order classical surface-diffusion equation in one spatial dimension. Moreover, the regularity and blow-up of solutions are also studied.