Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line
This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three p...
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Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/352159 |
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doaj-f502ab2e1c1e41f687b238a7e081f1f22020-11-24T22:59:59ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/352159352159Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole LineYuji Liu0Department of Mathematics, Guangdong University of Business Studies, Guangzhou 510320, ChinaThis paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x’(t))]’ involved with the function ρ, which makes the solutions un-concave.http://dx.doi.org/10.1155/2012/352159 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yuji Liu |
| spellingShingle |
Yuji Liu Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line Abstract and Applied Analysis |
| author_facet |
Yuji Liu |
| author_sort |
Yuji Liu |
| title |
Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line |
| title_short |
Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line |
| title_full |
Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line |
| title_fullStr |
Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line |
| title_full_unstemmed |
Multiple Bounded Positive Solutions to Integral Type BVPs for Singular Second Order ODEs on the Whole Line |
| title_sort |
multiple bounded positive solutions to integral type bvps for singular second order odes on the whole line |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2012-01-01 |
| description |
This paper is concerned with the integral type boundary value problems of the second order differential equations with one-dimensional p-Laplacian on the whole line. By constructing a suitable Banach space and a operator equation, sufficient conditions to guarantee the existence of at least three positive solutions of the BVPs are established. An example is presented to illustrate the main results. The emphasis is put on the one-dimensional p-Laplacian term [ρ(t)Φ(x’(t))]’ involved with the function ρ, which makes the solutions un-concave. |
| url |
http://dx.doi.org/10.1155/2012/352159 |
| work_keys_str_mv |
AT yujiliu multipleboundedpositivesolutionstointegraltypebvpsforsingularsecondorderodesonthewholeline |
| _version_ |
1725642940580102144 |