Entire Bounded Solutions for a Class of Quasilinear Elliptic Equations
We consider the problem −div(|∇u|p−2∇u)=a(x)(um+λun), x∈â„ÂN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2007-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://dx.doi.org/10.1155/2007/16407 |
| Summary: | We consider the problem −div(|∇u|p−2∇u)=a(x)(um+λun), x∈â„ÂN, N≥3, where 0<m<p−1<n,a(x)≥0, a(x) is not identically zero. Under the condition that a(x) satisfies (H), we show that there exists λ0>0 such that the above-mentioned equation admits at least one solution for all λ∈(0,λ0). This extends the results of Laplace equation to the case of p-Laplace equation. |
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| ISSN: | 1687-2762 1687-2770 |