Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities
We study the effect of the coefficient f(x) of the critical nonlinearity on the number of positive solutions for a p-q-Laplacian equation. Under suitable assumptions for f(x) and g(x), we should prove that for sufficiently small λ>0, there exist at least k positive solutions of the following p-q-...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/829069 |
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| Summary: | We study the effect of the coefficient f(x) of the critical nonlinearity on the number of positive solutions for a p-q-Laplacian equation. Under suitable assumptions for f(x) and g(x), we should prove that for sufficiently small λ>0, there exist at least k positive solutions of the following p-q-Laplacian equation, -Δpu-Δqu=fxu|p*-2u+λgxu|r-2u in Ω, u=0 on ∂Ω, where Ω⊂RN is a bounded smooth domain, N>p, 1<q<N(p-1)/(N-1)<p≤max{p,p^*-q/(p-1)}<r<p^*, p^*=Np/(N-p) is the critical Sobolev exponent, and Δsu=div(|∇u|s-2∇u is the s-Laplacian of u. |
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| ISSN: | 1085-3375 1687-0409 |