Green-Rvachev's quasi-function method for constructing two-sided approximations to positive solution of nonlinear boundary value problems
Keyword(s):
A homogeneous Dirichlet problem for a semilinear elliptic equations with the Laplace operator and Helmholtz operator is investigated. To construct the two-sided approximations to a positive solution of this boundary value problem the transition to an equivalent nonlinear integral equation (with the help of the Green-Rvachev's quasi-function) with its subsequent analysis by methods of the theory of semi-ordered spaces is used. The work and efficiency of the developed method are demonstrated by a computational experiment for a test problem with exponential nonlinearity.
Some nonlinear boundary value problems for nonlinear elliptic equations of second order in the plane
1985 ◽
Vol 4
(3)
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pp. 189-204
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2020 ◽
Vol 119
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1987 ◽
Vol 300
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pp. 287-287
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1990 ◽
Vol 147
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pp. 122-133
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