Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions
The multiple results of positive solutions for the following quasilinear elliptic equation: −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢+𝑔(𝑥)|𝑢|𝑝∗−2𝑢 in Ω,𝑢=0 on 𝜕Ω, are established. Here, 0∈Ω is a bounded smooth domain in ℝ𝑁,Δ𝑝 denotes the 𝑝-Laplacian operator, 1≤𝑞<𝑝<𝑁,𝑝∗=𝑁𝑝/(𝑁−𝑝),𝜆 is a positive real parameter, and 𝑓,...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/652109 |
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| _version_ | 1832565480668266496 |
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| author | Tsing-San Hsu |
| author_facet | Tsing-San Hsu |
| author_sort | Tsing-San Hsu |
| collection | DOAJ |
| description | The multiple results of positive solutions for the following quasilinear
elliptic equation: −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢+𝑔(𝑥)|𝑢|𝑝∗−2𝑢 in Ω,𝑢=0 on 𝜕Ω, are established. Here, 0∈Ω is a bounded smooth domain in ℝ𝑁,Δ𝑝 denotes the 𝑝-Laplacian operator, 1≤𝑞<𝑝<𝑁,𝑝∗=𝑁𝑝/(𝑁−𝑝),𝜆 is a positive real parameter, and 𝑓,𝑔 are continuous functions on Ω which are somewhere positive but which may change sign on Ω. The study is based on the extraction of Palais-Smale sequences in the Nehari manifold. |
| format | Article |
| id | doaj-art-ef5894cf03a94547890843c6bd47587b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ef5894cf03a94547890843c6bd47587b2025-02-03T01:07:33ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/652109652109Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight FunctionsTsing-San Hsu0Center for General Education, Chang Gung University, Kwei-Shan, Tao-Yuan 333, TaiwanThe multiple results of positive solutions for the following quasilinear elliptic equation: −Δ𝑝𝑢=𝜆𝑓(𝑥)|𝑢|𝑞−2𝑢+𝑔(𝑥)|𝑢|𝑝∗−2𝑢 in Ω,𝑢=0 on 𝜕Ω, are established. Here, 0∈Ω is a bounded smooth domain in ℝ𝑁,Δ𝑝 denotes the 𝑝-Laplacian operator, 1≤𝑞<𝑝<𝑁,𝑝∗=𝑁𝑝/(𝑁−𝑝),𝜆 is a positive real parameter, and 𝑓,𝑔 are continuous functions on Ω which are somewhere positive but which may change sign on Ω. The study is based on the extraction of Palais-Smale sequences in the Nehari manifold.http://dx.doi.org/10.1155/2009/652109 |
| spellingShingle | Tsing-San Hsu Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions Abstract and Applied Analysis |
| title | Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions |
| title_full | Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions |
| title_fullStr | Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions |
| title_full_unstemmed | Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions |
| title_short | Multiplicity Results for p-Laplacian with Critical Nonlinearity of Concave-Convex Type and Sign-Changing Weight Functions |
| title_sort | multiplicity results for p laplacian with critical nonlinearity of concave convex type and sign changing weight functions |
| url | http://dx.doi.org/10.1155/2009/652109 |
| work_keys_str_mv | AT tsingsanhsu multiplicityresultsforplaplacianwithcriticalnonlinearityofconcaveconvextypeandsignchangingweightfunctions |