ON THE \((p; q)\)-GROWTH OF ENTIRE FUNCTION SOLUTIONS OF HELMHOLTZ EQUATION

Volume 4, Issue 2, pp 92-101 http://dx.doi.org/10.22436/jnsa.004.02.01

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Authors

DEVENDRA KUMAR - Department of Mathematics, Research and Post Graduate Studies, M.M.H. College, Model Town, Ghaziabad 201001, U. P., India.

Abstract

The \((p; q)\)-growth of entire function solutions of Helmholtz equations in \(R^2\) has been studied. We obtain some lower bounds on order and type through function theoretic formulae related to those of associate. Our results extends and improve the results studied by McCoy [10].

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Keywords

• Index-pair \((p
• q)\)
• Bergman integral operator
• order and type
• Helmholtz equation and entire function.

MSC

•  35A35
•  35B05

References

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• [3] R. P. Gilbert, D. L. Colton, Integral operator methods in biaxial symmetric potential theory, Contrib. Differential Equations , 2 (1963), 441-456.


• [4] R. P. Gilbert, D. L. Colton, Singularities of solutions to elliptic partial differential equations, Quarterly J. Math., 19 (1968), 391-396.


• [5] O. P. Juneja, G. P. Kapoor, S. K. Bajpai , On the (p; q)-order and lower (p; q)-order of an entire function, J. Reine Angew. Math. , 282 (1976), 53-67.


• [6] O. P. Juneja, G. P. Kapoor, S. K. Bajpai , On the (p; q)-type and lower (p; q)-type of an entire function, J. Reine Angrew. Math. , 290 (1977), 180-190.


• [7] E. O. Kreyszig, M. Kracht, Methods of Complex Analysis in Partial Differential Equations with Applications, Canadian Math. Soc. Series of Monographs and Adv. Texts, John Wiley and Sons , New York (1988)


• [8] P. A. McCoy, Polynomial approximation and growth of generalized axisymmetric potentials, Canadian J. Math., XXXI (1979), 49-59.


• [9] P. A. McCoy, Optimal approximation and growth of solution to a class of elliptic differential equations, J. Math. Anal. Appl. , 154 (1991), 203-211.


• [10] P. A. McCoy, Solutions of the Helmholtz equation having rapid growth, Complex Variables and Elliptic Equations , 18 (1992), 91-101.