Multiple solutions for a problem with resonance involving the p-Laplacian
In this paper we will investigate the existence of multiple solutions for the problem (P) −Δpu+g(x,u)=λ1h(x)|u|p−2u, in Ω, u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | Abstract and Applied Analysis |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1085337598000517 |
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| Summary: | In this paper we will investigate the existence of multiple
solutions for the problem (P) −Δpu+g(x,u)=λ1h(x)|u|p−2u, in Ω, u∈H01,p(Ω) where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P). |
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| ISSN: | 1085-3375 |