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  Far East Journal of Applied Mathematics  
 ISSN: 0972-0960
 
 
 

     Far East Journal of Applied Mathematics
    Volume 35, Issue 1, Pages 65 - 79 (April 2009)


A NUMERICAL APPROACH TO FIND POSITIVE SOLUTIONS OF A SEMILINEAR ELLIPTIC EQUATION

S. Khademloo (Iran) and G. A. Afrouzi (Iran)

Received August 7, 2008

References:



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[2] M. Dehghan, Numerical procedures for a boundary value problem with a nonlinear boundary condition, Appl. Math. and Comput. 147 (2004), 291-306.

[3] F. Gazzola and A. Machiodi, Some remarks on equation for varying and p and varying domains, Communication in Partial Differential Equations 27(3, 4) (2002), 809-845.

[4] I. M. Gelfand, Some problems in the theory of quasi-linear equations, Amer. Math. Soc. Trans. 29(1) (1963), 295-381.

[5] D. D. Joseoh and T. S. Landgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal. 49 (1973), 241-269.

[6] D. D. Joseoh and E. M. Sparrow, Nonlinear diffusion induced by nonlinear sources, Quart. Appl. Math. 28 (1970), 327-342.

[7] H. B. Keller and D. S. Cohen, Some positive problems suggested by nonlinearheat generation, J. Math. Mech. 16 (1967), 1361-1376.

[8] O. A. Ladyzhenskaya, The Boundary Value Problems of Mathematical Physics, Springer-Verlag, New York, 1985.

[9] R. McOwen, Partial Differential Equations, Prentice-Hall, Inc., 1996.

[10] F. Mignot and J. P. Puel, Sur une classede problemes non lineairesavec nonlinearite positive, Croissante, Convexe, Comm. Part. Diff. Eq. 5(8) (1980), 791-836.

[11] D. J. Panov, Formulas for the Numerical Solution of the Partial Differential Equations by the Method of Differences, Fredrich Ungar Publishing Co., New York, 1951.

[12] I. G. Petrovsky, Lectures on Partial Differential Equations, Dover Publications, Inc., 1991.

Keywords and phrases: elliptic boundary value problems, multiple solutions, finite difference method, interpolation formula.

 


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