| Title:
|
Dead cores of singular Dirichlet boundary value problems with $\phi $-Laplacian (English) |
| Author:
|
Agarwal, Ravi P. |
| Author:
|
O'Regan, Donal |
| Author:
|
Staněk, Svatoslav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
53 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
381-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem $(\phi (u'))' = \lambda f(t,u,u')$, $u(0)=u(T)=A$. Here $\lambda $ is the positive parameter, $A>0$, $f$ is singular at the value $0$ of its first phase variable and may be singular at the value $A$ of its first and at the value $0$ of its second phase variable. (English) |
| Keyword:
|
singular Dirichlet boundary value problem |
| Keyword:
|
dead core |
| Keyword:
|
positive solution |
| Keyword:
|
dead core solution |
| Keyword:
|
pseudodead core solution |
| Keyword:
|
existence |
| Keyword:
|
$\phi $-Laplacian |
| MSC:
|
34B09 |
| MSC:
|
34B16 |
| MSC:
|
34B18 |
| idZBL:
|
Zbl 1199.34076 |
| idMR:
|
MR2433727 |
| DOI:
|
10.1007/s10492-008-0031-z |
| . |
| Date available:
|
2010-07-20T12:28:55Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140327 |
| . |
| Reference:
|
[1] Aris, R.: The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts.Clarendon Press Oxford (1975). Zbl 0315.76052 |
| Reference:
|
[2] Agarwal, R. P., O'Regan, D., Staněk, S.: General existence principles for nonlocal boundary value problems with $\phi$-Laplacian and their applications.Abstr. Appl. Anal. ID 96826 (2006), 1-30. Zbl 1147.34007, MR 2211656, 10.1155/AAA/2006/96826 |
| Reference:
|
[3] Agarwal, R. P., O'Regan, D., Staněk, S.: Positive and dead core solutions of singular Dirichlet boundary value problems with $\phi$-Laplacian.Comput. Math. Appl. 54 (2007), 255-266. MR 2337856, 10.1016/j.camwa.2006.12.026 |
| Reference:
|
[4] Baxley, J. V., Gersdorff, G. S.: Singular reaction-diffusion boundary value problems.J. Differ. Equations 115 (1995), 441-457. Zbl 0815.35019, MR 1310940, 10.1006/jdeq.1995.1022 |
| Reference:
|
[5] Bobisud, L. E.: Behavior of solutions for a Robin problem.J. Differential Equations 85 (1990), 91-104. Zbl 0704.34033, MR 1052329, 10.1016/0022-0396(90)90090-C |
| Reference:
|
[6] Bobisud, L. E.: Asymptotic dead cores for reaction-diffusion equations.J. Math. Anal. Appl. 147 (1990), 249-262. Zbl 0706.34052, MR 1044698, 10.1016/0022-247X(90)90396-W |
| Reference:
|
[7] Bobisud, L. E., O'Regan, D., Royalty, W. D.: Existence and nonexistence for a singular boundary value problem.Appl. Anal. 28 (1988), 245-256. Zbl 0628.34025, MR 0960389, 10.1080/00036818808839765 |
| Reference:
|
[8] Polášek, V., Rachůnková, I.: Singular Dirichlet problem for ordinary differential equations with $\phi$-Laplacian.Math. Bohem. 130 (2005), 409-425. Zbl 1114.34017, MR 2182386 |
| Reference:
|
[9] Wang, J., Gao, W.: Existence of solutions to boundary value problems for a nonlinear second order equation with weak Carathéodory functions.Differ. Equ. Dyn. Syst. 5 (1997), 175-185. Zbl 0891.34022, MR 1657262 |
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