A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application
We establish a new solution operator for the following problem -φp(u′)′=g, t∈(0,1), u(0)=0=u(1), where φp(x)=|x|p-2x, p>1. g may be singular at the boundary or change signs or may not be in L1(0,1) so that this solution operator can cover larger class of g than previously known ones. As an applic...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/243740 |
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| Summary: | We establish a new solution operator for the following problem -φp(u′)′=g, t∈(0,1), u(0)=0=u(1), where φp(x)=|x|p-2x, p>1. g may be singular at the boundary or change signs or may not be in L1(0,1) so that this solution operator can cover larger class of g than previously known ones. As an application, by checking complete continuity of the solution operator, we show the existence of nontrivial solutions for p-Laplacian φp(u′)′+λh(t)f(u(t))=0, t∈(0,1), u(0)=0=u(1), where λ>0 a parameter and f∈C(ℝ,ℝ) and f(0)>0 and h may change signs or may be beyond of L1(0,1). |
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| ISSN: | 1085-3375 1687-0409 |