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      KCI등재 SCIE SCOPUS

      ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS

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      https://www.riss.kr/link?id=A103361103

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      다국어 초록 (Multilingual Abstract)

      We investigate the stability of nonlinear differential equations of the form y(n)(x) = F(x, y(x), y′(x), . . . , y(n−1)(x)) with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is ...

      We investigate the stability of nonlinear differential equations of the form y(n)(x) = F(x, y(x), y′(x), . . . , y(n−1)(x)) with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

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      참고문헌 (Reference)

      1 J. Baker, "The stability of the equation f(x+y) = f(x)f(y)" 74 (74): 242-246, 1979

      2 V. A. Faˇiziev, "The space of (ψ,ϒ)-additive mappings on semigroups" 354 (354): 4455-4472, 2002

      3 V. Radu, "The fixed point alternative and the stability of functional equations" 4 (4): 91-96, 2003

      4 T. Aoki, "On the stability of the linear transformation in Banach spaces" 2 : 64-66, 1950

      5 Th. M. Rassias, "On the stability of the linear mapping in Banach spaces" 72 (72): 297-300, 1978

      6 C.-G. Park, "On the stability of the linear mapping in Banach modules" 275 (275): 711-720, 2002

      7 S.-M. Jung, "On the stability of the linear functional equation in a single variable on complete metric groups" 59 (59): 165-171, 2014

      8 D. H. Hyers, "On the stability of the linear functional equation" 27 : 222-224, 1941

      9 D. H. Hyers, "On the stability of differential expressions" 28 : 59-64, 1954

      10 O. Hatori, "On the best constant of Hyers-Ulam stability" 5 (5): 387-393, 2004

      1 J. Baker, "The stability of the equation f(x+y) = f(x)f(y)" 74 (74): 242-246, 1979

      2 V. A. Faˇiziev, "The space of (ψ,ϒ)-additive mappings on semigroups" 354 (354): 4455-4472, 2002

      3 V. Radu, "The fixed point alternative and the stability of functional equations" 4 (4): 91-96, 2003

      4 T. Aoki, "On the stability of the linear transformation in Banach spaces" 2 : 64-66, 1950

      5 Th. M. Rassias, "On the stability of the linear mapping in Banach spaces" 72 (72): 297-300, 1978

      6 C.-G. Park, "On the stability of the linear mapping in Banach modules" 275 (275): 711-720, 2002

      7 S.-M. Jung, "On the stability of the linear functional equation in a single variable on complete metric groups" 59 (59): 165-171, 2014

      8 D. H. Hyers, "On the stability of the linear functional equation" 27 : 222-224, 1941

      9 D. H. Hyers, "On the stability of differential expressions" 28 : 59-64, 1954

      10 O. Hatori, "On the best constant of Hyers-Ulam stability" 5 (5): 387-393, 2004

      11 T. Miura, "On the Hyers-Ulam stability of a differentiable map" 55 (55): 17-24, 2002

      12 Z. Gajda, "On stability of additive mappings" 14 : 431-434, 1991

      13 C. Alsina, "On some inequalities and stability results related to the exponential function" 2 (2): 373-380, 1998

      14 M. Omladiˇc, "On non linear perturbations of isometries" 303 (303): 617-628, 1995

      15 D. H. Hyers, "On approximate isometries" 51 : 288-292, 1945

      16 Y.-H. Lee, "On an n-dimensional mixed type additive and quadratic functional equation" 228 : 13-16, 2014

      17 M. Burger, "On Ulam stabiltity" 1-21, 2012

      18 Takeshi Miura, "Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y′ = λy" 대한수학회 41 (41): 995-1005, 2004

      19 D. Popa, "Hyers-Ulam stability of the linear differential operator with non-constant coefficients" 219 (219): 1562-1568, 2012

      20 T. Miura, "Hyers-Ulam stability of the first order linear differential equation for Banach space-valued holomorphic mappings" 3 (3): 377-385, 2007

      21 Y. Li, "Hyers-Ulam stability of nonhomogeneous linear differential equations of second order" 2009 : 7-, 2009

      22 T. Miura, "Hyers-Ulam stability of linear differential operator with constant coefficients" 258 : 90-96, 2003

      23 Y. Li, "Hyers-Ulam stability of linear differential equations y′′ = λ2y" 8 (8): 215-219, 2010

      24 Y. Li, "Hyers-Ulam stability of linear differential equations of second order" 23 (23): 306-309, 2010

      25 S.-M. Jung, "Hyers-Ulam stability of linear differential equations of first order. III" 311 (311): 139-146, 2005

      26 S.-M. Jung, "Hyers-Ulam stability of linear differential equations of first order. II" 19 (19): 854-858, 2006

      27 S.-M. Jung, "Hyers-Ulam stability of linear differential equations of first order" 17 (17): 1135-1140, 2004

      28 G. L. Forti, "Hyers-Ulam stability of functional equations in several variables" 50 (50): 143-190, 1995

      29 P. Gˇavrut¸ˇa, "Hyers-Ulam stability for second-order linear differ-ential equations with boundary conditions" 2011 (2011): 1-5, 2011

      30 T. Huuskonen, "Hyers-Ulam constants of Hilbert spaces" 153 (153): 31-40, 2002

      31 M. Obloza, "Hyers stability of the linear differential equation" 13 : 259-270, 1993

      32 Pl. Kannappan, "Functional Equations and Inequalities with Applications" Springer 2009

      33 M. Obloza, "Connections between Hyers and Lyapunov stability of the ordinary differential equations" 14 : 141-146, 1997

      34 D. G. Bourgin, "Classes of transformations and bordering transformations" 57 : 223-237, 1951

      35 D. H. Hyers, "Approximate isometries of the space of continuous functions" 48 : 285-289, 1947

      36 K. Ciepli´nski, "Applications of fixed point theorems to the Hyers-Ulam stability of func-tional equations – a survey" 3 (3): 151-164, 2012

      37 P. Gˇavrut¸ˇa, "A generalization of the Hyers-Ulam-Rassias stability of approximately ad-ditive mappings" 184 (184): 431-436, 1994

      38 K.-W. Jun, "A generalization of the Hyers-Ulam-Rassias stability of Jensen’s equation" 238 (238): 305-315, 1999

      39 J. B. Diaz, "A fixed point theorem of the alternative for contractions on a generalized complete metric space" 74 : 305-309, 1968

      40 S.-M. Jung, "A fixed point approach to the stability of differential equations y′ = F(x, y)" 33 (33): 47-56, 2010

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      2020-01-01 평가 등재학술지 유지 (해외등재 학술지 평가) KCI등재
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