Existence of Solutions for Nonlinear Elliptic Boundary Value Problems

SHAO Rong; NIU xin; SHEN Zu-he

Volume 24 Issue 1

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Abstract

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(1): 89-97

SHAO Rong, NIU xin, SHEN Zu-he. Existence of Solutions for Nonlinear Elliptic Boundary Value Problems[J]. Applied Mathematics and Mechanics, 2003, 24(1): 89-97.

Citation:

SHAO Rong, NIU xin, SHEN Zu-he. Existence of Solutions for Nonlinear Elliptic Boundary Value Problems[J]. Applied Mathematics and Mechanics, 2003, 24(1): 89-97.

Citation:

SHAO Rong, NIU xin, SHEN Zu-he. Existence of Solutions for Nonlinear Elliptic Boundary Value Problems[J]. Applied Mathematics and Mechanics, 2003, 24(1): 89-97.

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Existence of Solutions for Nonlinear Elliptic Boundary Value Problems

1.
Department of Mathematics, Nanjing University, Nanjing 210093, China;
2.
Department of Mathematics, Fuyang Teacher's College, Fuyang, Anhui 236032, China

Received Date: 2002-08-25
Rev Recd Date: 2002-09-30
Publish Date: 2003-01-15

Abstract

Abstract

Hilbert space method is applied to a class of semilinear second order elliptic boundary value problems and the existence of solutions is obtained with some restrictions.
- Hilbert space,
- coercivity condition,
- compact,
- imbedding mapping,
- elliptic equation

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References(6)

References

[1]	Kannan R,Locker J.On a class of nonlinear boundary value problems[J].J Differential Equations,1977,26(1):1-8.
[2]	Bates P W.Hilbert space methods for nonlinear elliptic equations[J].J Differential Equations,1979,32(2):250-257.
[3]	Hellwig G.Partial Differential Equations[M].New York:Blaisdell,1964.
[4]	Elcrat A R.Constructive Existence for semilinear elliptic equations with discontinuous coefficients[J].SIAM J Math Analysis,1974,5(4):663-672.
[5]	Alexiades V,Elcrat A R,Schaefer P W.Existence theorems for some nonlinear fourth order elliptic boundary value problems[J].Nonlinear Analysis,Theory,Methods &Applications,1980,4(4):805-813.
[6]	Agmon S.Lectures on Elliptic Boundary Value Problems[M].Princeton,New Jersey:D Van Nostrand Company,Inc,1965.

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