Results in Mathematics

, Volume 65, Issue 1–2, pp 95–103 | Cite as

Stability Properties in Some Classes of Second Order Partial Differential Equations

  • Eszter GselmannEmail author


The main purpose of this note is to investigate the stability problem in a certain class of partial differential equations.

Mathematics Subject Classification (2000)

39B82 39B52 35B35 


Stability partial differential equation Laplace’s equation elliptic equations 


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  1. 1.
    Alsina C., Ger R.: On some inequalities and stability results related to the exponential function. J. Inequal. Appl. 2(4), 373–380 (1998). doi: 10.1155/S102558349800023X zbMATHMathSciNetGoogle Scholar
  2. 2.
    András S., Kolumbán J.J.: On the Ulam-Hyers stability of first order differential systems with nonlocal initial conditions. Nonlinear Anal. 82, 1–11 (2013). doi: 10.1016/ CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Courant, R., Hilbert, D.: Methods of Mathematical Physics, vol. II. Wiley Classics Library. Wiley, New York (1989) (Partial differential equations, Reprint of the 1962 original, A Wiley-Interscience Publication)Google Scholar
  4. 4.
    Evans, L.C.: Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, 2nd edn. American Mathematical Society, Providence, RI (2010)Google Scholar
  5. 5.
    Găvruţă, P., Jung, S.M., Li, Y.: Hyers-Ulam stability for second-order linear differential equations with boundary conditions. Electron. J. Differ. Equ. 5 80 (2011)Google Scholar
  6. 6.
    Gilbarg, D., Trudinger, N.S.: Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer, Berlin (2001) (Reprint of the 1998 edition)Google Scholar
  7. 7.
    Hegyi B., Jung S.M.: On the stability of Laplace’s equation. Appl. Math. Lett. 26(5), 549–552 (2013). doi: 10.1016/j.aml.2012.12.014 CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Hyers D.H.: On the stability of the linear functional equation. Proc. Nat. Acad. Sci. USA 27, 222–224 (1941)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Jung S.M.: A fixed point approach to the stability of differential equations y′ = F(x, y). Bull. Malays. Math. Sci. Soc. (2) 33(1), 47–56 (2010)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Jung, S.M.: Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer Optimization and its Applications, vol. 48. Springer, New York (2011). doi: 10.1007/978-1-4419-9637-4
  11. 11.
    Jung S.M.: Approximate solutions of a linear differential equation of third order. Bull. Malays. Math. Sci. Soc. (2) 35(4), 1063–1073 (2012)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Kačur, J.: Method of Rothe in evolution equations, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], vol. 80. BSB B. G. Teubner Verlagsgesellschaft, Leipzig (1985) (With German, French and Russian summaries)Google Scholar
  13. 13.
    Lax P.D.: On the existence of Green’s function. Proc. Am. Math. Soc. 3, 526–531 (1952)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Polyanin A.D.: Handbook of Linear Partial Differential Equations for Engineers and Scientists. Chapman & Hall/CRC, Boca Raton (2002)zbMATHGoogle Scholar
  15. 15.
    Prástaro A., Rassias T.M.: Ulam stability in geometry of PDE’s. Nonlinear Funct. Anal. Appl. 8(2), 259–278 (2003)zbMATHMathSciNetGoogle Scholar
  16. 16.
    Rezaei H., Jung S.M., Rassias T.M.: Laplace transform and Hyers–Ulam stability of linear differential equations. J. Math. Anal. Appl. 403(1), 244–251 (2013). doi: 10.1016/j.jmaa.2013.02.034 CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of DebrecenDebrecenHungary

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