• Title/Summary/Keyword: Differential inequality

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GEOMETRIC INEQUALITIES FOR SUBMANIFOLDS IN SASAKIAN SPACE FORMS

  • Presura, Ileana
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1095-1103
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    • 2016
  • B. Y. Chen introduced a series of curvature invariants, known as Chen invariants, and proved sharp estimates for these intrinsic invariants in terms of the main extrinsic invariant, the squared mean curvature, for submanifolds in Riemannian space forms. Special classes of submanifolds in Sasakian manifolds play an important role in contact geometry. F. Defever, I. Mihai and L. Verstraelen [8] established Chen first inequality for C-totally real submanifolds in Sasakian space forms. Also, the differential geometry of slant submanifolds has shown an increasing development since B. Y. Chen defined slant submanifolds in complex manifolds as a generalization of both holomorphic and totally real submanifolds. The slant submanifolds of an almost contact metric manifolds were defined and studied by A. Lotta, J. L. Cabrerizo et al. A Chen first inequality for slant submanifolds in Sasakian space forms was established by A. Carriazo [4]. In this article, we improve this Chen first inequality for special contact slant submanifolds in Sasakian space forms.

BOUNDEDNESS FOR PERTURBED DIFFERENTIAL EQUATIONS VIA LYAPUNOV EXPONENTS

  • Choi, Sung Kyu;Kim, Jiheun;Koo, Namjip;Ryu, Chunmi
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.589-597
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    • 2012
  • In this paper we investigate the stability of solutions of the perturbed differential equations with the positive order of the perturbation by using the notion of the Lyapunov exponent of unperturbed equations and an integral inequality of Bihari type.

EVOLUTION EQUATIONS ON A RIEMANNIAN MANIFOLD WITH A LOWER RICCI CURVATURE BOUND

  • Chang, Jeongwook
    • East Asian mathematical journal
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    • v.30 no.1
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    • pp.79-91
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    • 2014
  • We consider the parabolic evolution differential equation such as heat equation and porus-medium equation on a Riemannian manifold M whose Ricci curvature is bounded below by $-(n-1)k^2$ and bounded below by 0 on some amount of M. We derive some bounds of differential quantities for a positive solution and some inequalities which resemble Harnack inequalities.

TWO COMPARISON THEOREMS OF BSDES

  • Huang, Xiao-Qin;Wang, Mian-Sen;Jia, Jun-Guo
    • Journal of applied mathematics & informatics
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    • v.24 no.1_2
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    • pp.377-385
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    • 2007
  • In this paper, by the equations of Mao [9] and Peng [5], we use the martingale method to establish the comparison theorems of backward stochastic differential equations (BSDEs). We generalize the results of Cao-Yan [1].

WEIGHTED PSEUDO ALMOST PERIODIC SOLUTIONS OF HOPFIELD ARTIFICIAL NEURAL NETWORKS WITH LEAKAGE DELAY TERMS

  • Lee, Hyun Mork
    • Journal of the Chungcheong Mathematical Society
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    • v.34 no.3
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    • pp.221-234
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    • 2021
  • We introduce high-order Hopfield neural networks with Leakage delays. Furthermore, we study the uniqueness and existence of Hopfield artificial neural networks having the weighted pseudo almost periodic forcing terms on finite delay. Our analysis is based on the differential inequality techniques and the Banach contraction mapping principle.

ANALYSIS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL INTEGRODIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES

  • KARTHIKEYAN, K.;RAJA, D. SENTHIL;SUNDARARAJAN, P.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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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.

THE ZEROS OF SOLUTIONS OF SOME DIFFERENTIAL INEQUALITIES

  • Kim, RakJoong
    • Korean Journal of Mathematics
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    • v.11 no.2
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    • pp.117-125
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    • 2003
  • Let $x(t)$ satisty $$(p(t)x^{\prime}(t))^{\prime}+q(t)x^{{\alpha}}(t)+r(t)x^{{\beta}-1}x^{\prime}(t){\leq}0({\geq}0)$$. Then the zeros of $x(t)$ or $x^{\prime}(t)$ are simple.

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