Infinite semipositone problems with a falling zero and nonlinear boundary conditions
We consider the problem $$\displaylines{ -u'' =h(t)\big(\frac{au-u^{2}-c}{u^\alpha}\big) , \quad t \in (0, 1),\cr u(0) = 0, \quad u'(1)+g(u(1))=0, }$$ where $a>0$, $c\geq 0$, $\alpha \in (0, 1)$, $h{:}(0, 1] \to (0, \infty)$ is a continuous function which may be singular at...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/193/abstr.html |
| _version_ | 1818067668582793216 |
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| author | Mohan Mallick Lakshmi Sankar Ratnasingham Shivaji Subbiah Sundar |
| author_facet | Mohan Mallick Lakshmi Sankar Ratnasingham Shivaji Subbiah Sundar |
| author_sort | Mohan Mallick |
| collection | DOAJ |
| description | We consider the problem
$$\displaylines{
-u'' =h(t)\big(\frac{au-u^{2}-c}{u^\alpha}\big) , \quad t \in (0, 1),\cr
u(0) = 0, \quad u'(1)+g(u(1))=0,
}$$
where $a>0$, $c\geq 0$, $\alpha \in (0, 1)$, $h{:}(0, 1] \to (0, \infty)$
is a continuous function which may be singular at $t=0$, but belongs to
$L^1(0, 1)\cap C^1(0,1)$, and $g{:}[0, \infty) \to [0, \infty)$ is a continuous
function. We discuss existence, uniqueness, and non existence results for
positive solutions for certain values of a, b and c. |
| first_indexed | 2024-12-10T15:27:20Z |
| format | Article |
| id | doaj.art-fd9881c34dc44a7cb51a41dea5827939 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T15:27:20Z |
| publishDate | 2018-11-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-fd9881c34dc44a7cb51a41dea58279392022-12-22T01:43:30ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-11-012018193,113Infinite semipositone problems with a falling zero and nonlinear boundary conditionsMohan Mallick0Lakshmi Sankar1Ratnasingham Shivaji2Subbiah Sundar3 IIT Madras, Chennai, India Univ. of North Carolina, Greensboro, NC, USA IIT Madras, Chennai, India We consider the problem $$\displaylines{ -u'' =h(t)\big(\frac{au-u^{2}-c}{u^\alpha}\big) , \quad t \in (0, 1),\cr u(0) = 0, \quad u'(1)+g(u(1))=0, }$$ where $a>0$, $c\geq 0$, $\alpha \in (0, 1)$, $h{:}(0, 1] \to (0, \infty)$ is a continuous function which may be singular at $t=0$, but belongs to $L^1(0, 1)\cap C^1(0,1)$, and $g{:}[0, \infty) \to [0, \infty)$ is a continuous function. We discuss existence, uniqueness, and non existence results for positive solutions for certain values of a, b and c.http://ejde.math.txstate.edu/Volumes/2018/193/abstr.htmlInfinite semipostioneexterior domainsub and super solutionsnonlinear boundary conditions |
| spellingShingle | Mohan Mallick Lakshmi Sankar Ratnasingham Shivaji Subbiah Sundar Infinite semipositone problems with a falling zero and nonlinear boundary conditions Electronic Journal of Differential Equations Infinite semipostione exterior domain sub and super solutions nonlinear boundary conditions |
| title | Infinite semipositone problems with a falling zero and nonlinear boundary conditions |
| title_full | Infinite semipositone problems with a falling zero and nonlinear boundary conditions |
| title_fullStr | Infinite semipositone problems with a falling zero and nonlinear boundary conditions |
| title_full_unstemmed | Infinite semipositone problems with a falling zero and nonlinear boundary conditions |
| title_short | Infinite semipositone problems with a falling zero and nonlinear boundary conditions |
| title_sort | infinite semipositone problems with a falling zero and nonlinear boundary conditions |
| topic | Infinite semipostione exterior domain sub and super solutions nonlinear boundary conditions |
| url | http://ejde.math.txstate.edu/Volumes/2018/193/abstr.html |
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