Geodesic
ON THE $(p; q)$-GROWTH OF ENTIRE FUNCTION SOLUTIONS OF HELMHOLTZ EQUATION
KUMAR, DEVENDRA1
1 Department of Mathematics, Research and Post Graduate Studies, M.M.H. College, Model Town, Ghaziabad 201001, U. P., India
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 2, p. 92-101.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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].
DOI : 10.22436/jnsa.004.02.01
Classification : 35A35, 35B05
Keywords: Index-pair \((p, q)\), Bergman integral operator, order and type, Helmholtz equation and entire function.

KUMAR, DEVENDRA 1

1 Department of Mathematics, Research and Post Graduate Studies, M.M.H. College, Model Town, Ghaziabad 201001, U. P., India 
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KUMAR, DEVENDRA. ON THE \((p; q)\)-GROWTH OF ENTIRE FUNCTION SOLUTIONS OF HELMHOLTZ EQUATION. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 2, p. 92-101. doi : 10.22436/jnsa.004.02.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.02.01/

[1] Bergman, S. Integral operators in the Theory of Linear Partial Differential Equations, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 23, Springer-Verlag, New Yok, 1969

[2] Gilbert, R. P. Function Theoretic Methods in Partial Differential Equations, Math. in Science and Engineering Vol. 54, Academic Press, New York, 1969

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

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

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

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

[7] Kreyszig, E. O.; Kracht, M. 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] McCoy, P. A. Polynomial approximation and growth of generalized axisymmetric potentials, Canadian J. Math., Volume XXXI (1979), pp. 49-59

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

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

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