On the continuity of principal eigenvalues for boundary value problems with indefinite weight function with respect to radius of balls in ℝN
We investigate the continuity of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem −Δu(x)=λg(x)u(x), x∈BR(0);u(x)=0, |x|=R, where BR(0) is a ball in ℝN, and g is a smooth function, and we show that λ1+(R) and λ1−(R) are continuous funct...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007147 |
| Summary: | We investigate the continuity of principal eigenvalues (i.e.,
eigenvalues corresponding to positive eigenfunctions) for the
boundary value problem −Δu(x)=λg(x)u(x), x∈BR(0);u(x)=0, |x|=R, where BR(0) is a ball in ℝN, and g is a smooth function, and we show that λ1+(R) and λ1−(R) are continuous functions of R. |
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| ISSN: | 0161-1712 1687-0425 |