| Title:
|
Existence of solutions for the Dirichlet problem with superlinear nonlinearities (English) |
| Author:
|
Nowakowski, Andrzej |
| Author:
|
Rogowski, Andrzej |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
515-528 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we establish the existence of nontrivial solutions to \[\frac{\mathrm d}{{\mathrm d}t}L_{x^{\prime }}(t,x^{\prime }(t))+V_{x} (t,x(t))=0,\quad x(0)=0=x(T),\] with $V_x$ superlinear in $x$. (English) |
| Keyword:
|
nonlinear Dirichlet problem |
| Keyword:
|
nontrivial solution |
| Keyword:
|
duality method |
| Keyword:
|
superlinear nonlinearity |
| MSC:
|
34B15 |
| MSC:
|
47J30 |
| MSC:
|
49J40 |
| idZBL:
|
Zbl 1080.34516 |
| idMR:
|
MR2000049 |
| . |
| Date available:
|
2009-09-24T11:03:57Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127819 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/128001 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] S. K. Ingram: Continuous dependence on parameters and boundary value problems.Pacific J. Math. 41 (1972), 395–408. MR 0304741, 10.2140/pjm.1972.41.395 |
| Reference:
|
[4] G. Klaasen: Dependence of solutions on boundary conditions for second order ordinary differential equations.J. Differential Equations 7 (1970), 24–33. Zbl 0184.11704, MR 0273086, 10.1016/0022-0396(70)90121-X |
| Reference:
|
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| Reference:
|
[6] J. Mawhin: Problèmes de Dirichlet Variationnels Non Linéares.Les Presses de l’Université de Montréal, 1987. MR 0906453 |
| Reference:
|
[7] A. Nowakowski: A new variational principle and duality for periodic solutions of Hamilton’s equations.J. Differential Equations 97 (1992), 174–188. Zbl 0759.34039, MR 1161317, 10.1016/0022-0396(92)90089-6 |
| Reference:
|
[8] P. H. Rabinowitz: Minimax Methods in Critical Points Theory with Applications to Differential Equations.AMS, Providence, 1986. MR 0845785 |
| Reference:
|
[9] D. O’Regan: Singular Dirichlet boundary value problems. I. Superlinear and nonresonant case.Nonlinear Anal. 29 (1997), 221–245. MR 1446226, 10.1016/S0362-546X(96)00026-0 |
| . |
