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Linear Boundary Value Problems

  • Ravi P. AgarwalEmail author
  • Simona Hodis
  • Donal O’Regan
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

We begin this chapter by showing that solutions of second-order linear boundary value problems exist (and analogously for the higher order) if and only if corresponding systems of algebraic equations of second (higher) order have solutions. Then, we shall use the method of separation of variables also known as the Fourier method (after Jean Baptiste Joseph Fourier (1768–1830)) to solve some basic partial differential equations. An important feature of this method is that it leads to finding the solutions of boundary value problems for ordinary differential equations. We shall also consider problems in infinite domains which can be effectively solved by finding the Fourier transform, or the Fourier sine or cosine transform of the unknown function.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ravi P. Agarwal
    • 1
    Email author
  • Simona Hodis
    • 1
  • Donal O’Regan
    • 2
  1. 1.Department of MathematicsTexas A&M University–KingsvilleKingsvilleUSA
  2. 2.Department of MathematicsNational University of IrelandGalwayIreland

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