Existence and L∞ estimates of some Mountain-Pass type solutions
ESAIM: Control, Optimisation and Calculus of Variations (2009)
- Volume: 15, Issue: 3, page 499-508
- ISSN: 1292-8119
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topGomes, José Maria. "Existence and L∞ estimates of some Mountain-Pass type solutions." ESAIM: Control, Optimisation and Calculus of Variations 15.3 (2009): 499-508. <http://eudml.org/doc/250569>.
@article{Gomes2009,
abstract = {
We prove the existence of a positive solution to the BVP
$$(\Phi(t)u'(t))'=f(t,u(t)),\,\,\,\,\,\,\,\,\,\,\,u'(0)=u(1)=0, $$
imposing some conditions on Φ and f. In particular, we
assume $\Phi(t)f(t,u)$ to be decreasing in t. Our method
combines variational and topological arguments and can be applied
to some elliptic problems in annular domains. An $L_\infty$ bound
for the solution is provided by the $L_\infty$ norm of any test
function with negative energy.
},
author = {Gomes, José Maria},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Second order singular differential
equation; variational methods; Mountain Pass Theorem; second order singular differential equation; mountain pass theorem; estimates; elliptic problem in annulus},
language = {eng},
month = {7},
number = {3},
pages = {499-508},
publisher = {EDP Sciences},
title = {Existence and L∞ estimates of some Mountain-Pass type solutions},
url = {http://eudml.org/doc/250569},
volume = {15},
year = {2009},
}
TY - JOUR
AU - Gomes, José Maria
TI - Existence and L∞ estimates of some Mountain-Pass type solutions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2009/7//
PB - EDP Sciences
VL - 15
IS - 3
SP - 499
EP - 508
AB -
We prove the existence of a positive solution to the BVP
$$(\Phi(t)u'(t))'=f(t,u(t)),\,\,\,\,\,\,\,\,\,\,\,u'(0)=u(1)=0, $$
imposing some conditions on Φ and f. In particular, we
assume $\Phi(t)f(t,u)$ to be decreasing in t. Our method
combines variational and topological arguments and can be applied
to some elliptic problems in annular domains. An $L_\infty$ bound
for the solution is provided by the $L_\infty$ norm of any test
function with negative energy.
LA - eng
KW - Second order singular differential
equation; variational methods; Mountain Pass Theorem; second order singular differential equation; mountain pass theorem; estimates; elliptic problem in annulus
UR - http://eudml.org/doc/250569
ER -
References
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