• Journal of applied mathematics & informatics
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• 제42권2호
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• pp.305-320
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• 2024

We consider a mathematical model which describes the quasistatic contact of electro-viscoelastic rod with an obstacle. We use a modified Kelvin-Voigt viscoelastic constitutive law in which the elasticity operator is nonlinear and locally Lipschitz continuous, taking into account the piezoelectric effect of the material. We model the contact with a general damped response condition. We establish a local existence and uniqueness result of the solution by using arguments of time-dependent nonlinear equations and Schauder's fixed-point theorem and obtain a global existence for small enough data.

• 대한수학회보
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• 제34권3호
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• pp.411-419
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• 1997

Using the theory of strongly continuous cosine families, we prove controllable of nonlinear second order control system and give an application.

• East Asian mathematical journal
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• 제15권1호
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• pp.91-103
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• 1999

• 대한수학회지
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• 제39권4호
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• pp.579-591
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• 2002

New fixed Point results for the (equation omitted) selfmaps ale given. The analysis relies on a factorization idea. The notion of an essential map is also introduced for a wide class of maps. Finally, from a new fixed point theorem of ours, we deduce some equilibrium theorems.

• 대한수학회논문집
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• 제37권2호
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• East Asian mathematical journal
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• 제31권5호
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• pp.727-735
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• 2015

We introduce the fundamental theorem of upper and lower solutions for a class of singular ($p_1,\;p_2$)-Laplacian systems and give the proof by using the Schauder fixed point theorem. It will play an important role to study the existence of solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.85-93
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• 2007

In this paper we prove the existence of mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed point theorem.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.305-316
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• 2022

We study the existence and uniqueness of solutions for a class of boundary value problems of nonlinear fractional order differential equations involving the Caputo fractional derivative by employing the Banach's contraction principle and the Schauder's fixed point theorem. In addition, an example is given to demonstrate the application of our main results.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.165-177
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• 2024

In this paper, we investigate the suitable conditions for the existence results for a class of 𝔍-Hilfer fractional nonlinear Fredholm-Volterra models with new conditions. The findings are based on Banach contraction principle and Schauder's fixed point theorem. Also, the generalized Hyers-Ulam stability and generalized Hyers-Ulam-Rassias stability for solutions of the given problem are provided.