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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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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| author | Inbo Sim Yong Hoon Lee |
| author_facet | Inbo Sim Yong Hoon Lee |
| author_sort | Inbo Sim |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-a1a11443ca2b40199dc8a64809e1227f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a1a11443ca2b40199dc8a64809e1227f2025-02-03T01:13:01ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/243740243740A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its ApplicationInbo Sim0Yong Hoon Lee1Department of Mathematics, University of Ulsan, Ulsan 680-749, Republic of KoreaDepartment of Mathematics, Pusan National University, Busan 609-735, Republic of KoreaWe 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).http://dx.doi.org/10.1155/2012/243740 |
| spellingShingle | Inbo Sim Yong Hoon Lee A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application Abstract and Applied Analysis |
| title | A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application |
| title_full | A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application |
| title_fullStr | A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application |
| title_full_unstemmed | A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application |
| title_short | A New Solution Operator of One-Dimensional p-Laplacian with a Sign-Changing Weight and Its Application |
| title_sort | new solution operator of one dimensional p laplacian with a sign changing weight and its application |
| url | http://dx.doi.org/10.1155/2012/243740 |
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