Existence of solutions for the Dirichlet problem with superlinear nonlinearities
Andrzej Nowakowski; Andrzej Rogowski
Czechoslovak Mathematical Journal (2003)
- Volume: 53, Issue: 3, page 515-528
- ISSN: 0011-4642
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topNowakowski, Andrzej, and Rogowski, Andrzej. "Existence of solutions for the Dirichlet problem with superlinear nonlinearities." Czechoslovak Mathematical Journal 53.3 (2003): 515-528. <http://eudml.org/doc/30795>.
@article{Nowakowski2003,
abstract = {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 $x$.},
author = {Nowakowski, Andrzej, Rogowski, Andrzej},
journal = {Czechoslovak Mathematical Journal},
keywords = {nonlinear Dirichlet problem; nontrivial solution; duality method; superlinear nonlinearity; nonlinear Dirichlet problem; nontrivial solution; duality method; superlinear nonlinearity},
language = {eng},
number = {3},
pages = {515-528},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of solutions for the Dirichlet problem with superlinear nonlinearities},
url = {http://eudml.org/doc/30795},
volume = {53},
year = {2003},
}
TY - JOUR
AU - Nowakowski, Andrzej
AU - Rogowski, Andrzej
TI - Existence of solutions for the Dirichlet problem with superlinear nonlinearities
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 515
EP - 528
AB - 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 $x$.
LA - eng
KW - nonlinear Dirichlet problem; nontrivial solution; duality method; superlinear nonlinearity; nonlinear Dirichlet problem; nontrivial solution; duality method; superlinear nonlinearity
UR - http://eudml.org/doc/30795
ER -
References
top- Boundary value problems for forced superlinear second order ordinary differential equations, Nonlinear Partial Differential Equations and Their Applications. College de France Seminar, Vol. XII, Pitman Res. Notes ser., 302, 1994, pp. 55–64. (1994) MR1291842
- 10.1216/rmjm/1181071858, Rocky Mountain J. Math. 27 (1997), 1041–1053. (1997) MR1627654DOI10.1216/rmjm/1181071858
- 10.2140/pjm.1972.41.395, Pacific J. Math. 41 (1972), 395–408. (1972) MR0304741DOI10.2140/pjm.1972.41.395
- 10.1016/0022-0396(70)90121-X, J. Differential Equations 7 (1970), 24–33. (1970) Zbl0184.11704MR0273086DOI10.1016/0022-0396(70)90121-X
- 10.1016/0022-0396(91)90020-A, J. Differential Equations 93 (1991), 1–18. (1991) MR1122304DOI10.1016/0022-0396(91)90020-A
- Problèmes de Dirichlet Variationnels Non Linéares, Les Presses de l’Université de Montréal, 1987. (1987) MR0906453
- 10.1016/0022-0396(92)90089-6, J. Differential Equations 97 (1992), 174–188. (1992) Zbl0759.34039MR1161317DOI10.1016/0022-0396(92)90089-6
- Minimax Methods in Critical Points Theory with Applications to Differential Equations, AMS, Providence, 1986. (1986) MR0845785
- 10.1016/S0362-546X(96)00026-0, Nonlinear Anal. 29 (1997), 221–245. (1997) MR1446226DOI10.1016/S0362-546X(96)00026-0
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