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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| Format: | Article |
| Language: | English |
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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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| author | Tsing-San Hsu Huei-Li Lin |
| author_facet | Tsing-San Hsu Huei-Li Lin |
| author_sort | Tsing-San Hsu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-680958640cd445c49532931529dc4917 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-680958640cd445c49532931529dc49172025-02-03T06:01:22ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/829069829069Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical NonlinearitiesTsing-San Hsu0Huei-Li Lin1Division of Natural Science, Center for General Education, Chang Gung University, Taoyuan 333, TaiwanDivision of Natural Science, Center for General Education, Chang Gung University, Taoyuan 333, TaiwanWe 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.http://dx.doi.org/10.1155/2014/829069 |
| spellingShingle | Tsing-San Hsu Huei-Li Lin Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities Abstract and Applied Analysis |
| title | Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities |
| title_full | Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities |
| title_fullStr | Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities |
| title_full_unstemmed | Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities |
| title_short | Multiplicity of Positive Solutions for a p-q-Laplacian Type Equation with Critical Nonlinearities |
| title_sort | multiplicity of positive solutions for a p q laplacian type equation with critical nonlinearities |
| url | http://dx.doi.org/10.1155/2014/829069 |
| work_keys_str_mv | AT tsingsanhsu multiplicityofpositivesolutionsforapqlaplaciantypeequationwithcriticalnonlinearities AT hueililin multiplicityofpositivesolutionsforapqlaplaciantypeequationwithcriticalnonlinearities |