Hyers–Ulam stability of a first order partial differential equation

Abstract We prove that the existence of a global prime integral leads, in appropriate conditions, to the Hyers–Ulam stability of a linear partial differential equation of first order.

[1]  Dorian Popa,et al.  The Hyers–Ulam stability of nonlinear recurrences , 2007 .

[2]  Hiroyuki Takagi,et al.  The Hyers–Ulam stability constants of first order linear differential operators , 2004 .

[3]  Soon-Mo Jung,et al.  Hyers-Ulam stability of linear differential equations of first order, II , 2006, Appl. Math. Lett..

[4]  S.-M. Jung,et al.  Hyers-Ulam stability of linear partial differential equations of first order , 2009, Appl. Math. Lett..

[5]  Takeshi Miura,et al.  ON THE HYERS-ULAM STABILITY OF THE BANACH SPACE-VALUED DIFFERENTIAL EQUATION y'=λy , 2002 .

[6]  George Isac,et al.  Stability of Functional Equations in Several Variables , 1998 .

[7]  T. Rassias.  On the stability of the linear mapping in Banach spaces , 1978 .

[8]  Soon-Mo Jung,et al.  Hyers–Ulam stability of a system of first order linear differential equations with constant coefficients☆ , 2006 .

[9]  Tosio Aoki,et al.  On the Stability of the linear Transformation in Banach Spaces. , 1950 .

[10]  Dorian Popa.  Hyers-Ulam-Rassias stability of a linear recurrence , 2005 .

[11]  S. Czerwik,et al.  Functional equations and inequalities in several variables , 2002 .

[12]  Takeshi Miura,et al.  A characterization of Hyers–Ulam stability of first order linear differential operators , 2003 .

[13]  Ioan A. Rus,et al.  REMARKS ON ULAM STABILITY OF THE OPERATORIAL EQUATIONS , 2009 .

[14]  D. H. Hyers.  On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Soon-Mo Jung,et al.  Hyers-Ulam stability of first order linear partial differential equations with constant coefficients , 2007 .

[16]  S. Ulam.  A collection of mathematical problems , 1960 .

[17]  Soon-Mo Jung,et al.  Hyers-Ulam stability of linear differential equations of first order, III , 2005 .

[18]  Takeshi Miura,et al.  Hyers–Ulam stability of linear differential operator with constant coefficients , 2003 .

[19]  Claudi Alsina,et al.  On Some Inequalities and Stability Results Related to the Exponential Function , 1998 .