On the Existence, Uniqueness, and Basis Properties of Radial Eigenfunctions of a Semilinear Second-Order Elliptic Equation in a Ball
We consider the following eigenvalue problem: −Δ𝑢+𝑓(𝑢)=𝜆𝑢, 𝑢=𝑢(𝑥), 𝑥∈𝐵={𝑥∈ℝ3∶|𝑥|<1}, 𝑢(0)=𝑝>0, 𝑢||𝑥|=1=0, where 𝑝 is an arbitrary fixed parameter and 𝑓 is an odd smooth function. First, we prove that for each integer 𝑛≥0 there exists a radially symmetric eigenfunction 𝑢𝑛 which possesses prec...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/243048 |