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Eigenvalue problems for fourth order differential equations

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Summary

This paper is concerned with eigenvalue problems for fourth order differential equations representable by systems of the form:

$$x'' + q_{11} (t,\lambda )x + q_{12} (t,\lambda )y = 0, y'' + q_{21} (t,\lambda )x + q_{22} (t,\lambda )y = 0$$

. The boundary conditions are x(a)=y(a)=0=x(b)=y(b) or x(a)=y(a)=0=x′(a)=y′(b). Sufficient conditions for existence of least eigenvalues are given and their properties are discussed.

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Entrata in Redazione il 10 novembre 1976.

Acknowledgement: This will acknowledge the partial support of the author by the National Research Council of Canada under Grant number A3105 (1976–1977).

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Cheng, S. Eigenvalue problems for fourth order differential equations. Annali di Matematica 115, 329–340 (1977). https://doi.org/10.1007/BF02414724

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Keywords

  • Boundary Condition
  • Differential Equation
  • Eigenvalue Problem
  • Fourth Order
  • Order Differential Equation