A Note on Nonlocal Boundary Value Problems for Hyperbolic Schrödinger Equations

Yildirim Ozdemir and Mehmet Kucukunal

Abstract and Applied Analysis, 2012, vol. 2012, 1-12

Abstract:

The nonlocal boundary value problem ð ‘‘ 2 ð ‘¢ ( ð ‘¡ ) / ð ‘‘ ð ‘¡ 2 + ð ´ ð ‘¢ ( ð ‘¡ ) = ð ‘“ ( ð ‘¡ ) ( 0 ≤ ð ‘¡ ≤ 1 ) , ð ‘– ( ð ‘‘ ð ‘¢ ( ð ‘¡ ) / ð ‘‘ ð ‘¡ ) + ð ´ ð ‘¢ ( ð ‘¡ ) = ð ‘” ( ð ‘¡ ) ( − 1 ≤ ð ‘¡ ≤ 0 ) , ð ‘¢ ( 0 + ) = ð ‘¢ ( 0 − ) , ð ‘¢ ð ‘¡ ( 0 + ) = ð ‘¢ ð ‘¡ ( 0 − ) , ð ´ ð ‘¢ ( − 1 ) = ð ›¼ ð ‘¢ ( 𠜇 ) + 𠜑 , 0 < 𠜇 ≤ 1 , for hyperbolic Schrödinger equations in a Hilbert space ð » with the self-adjoint positive definite operator ð ´ is considered. The stability estimates for the solution of this problem are established. In applications, the stability estimates for solutions of the mixed-type boundary value problems for hyperbolic Schrödinger equations are obtained.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:687321

DOI: 10.1155/2012/687321

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