| Title:
|
Singular Dirichlet boundary value problems. II: Resonance case (English) |
| Author:
|
O'Regan, Donal |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
269-289 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Existence results are established for the resonant problem $y^{\prime \prime }+\lambda _m \,a\,y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in L_{{\mathrm loc}}^1(0,1)$ with $a>0$ a.e. on $[0,1]$ and $\int ^1_0 x(1-x)a(x)\,\mathrm{d}x <\infty $. (English) |
| MSC:
|
34B15 |
| MSC:
|
34L30 |
| idZBL:
|
Zbl 0957.34016 |
| idMR:
|
MR1624319 |
| . |
| Date available:
|
2009-09-24T10:13:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127416 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Mawhin, J., and Ward, J.R.: Nonuniform nonresonance conditions at the first two eigenvalues for periodic solutions of forced Liénard and Duffing equations.Rocky M.J. Math. 112 (1982), 643–654. 10.1216/RMJ-1982-12-4-643 |
| Reference:
|
[9] Naimark, M.A.: Linear differential operators, Part II.Ungar Publ. Co., London, 1968. Zbl 0227.34020, MR 0262880 |
| Reference:
|
[10] O’Regan, D.: Theory of singular boundary value problems.World Scientific Press, Singapore, 1994. |
| Reference:
|
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| Reference:
|
[12] O’Regan, D.: Singular Dirichlet boundary value problems I: Superlinear and nonresonance case.Nonlinear Analysis 29 (1997), 221–245. MR 1446226, 10.1016/S0362-546X(96)00026-0 |
| . |
