The Dirichlet problem with sublinear nonlinearities

Aleksandra Orpel. "The Dirichlet problem with sublinear nonlinearities." Annales Polonici Mathematici 78.2 (2002): 131-140. <http://eudml.org/doc/280968>.

@article{AleksandraOrpel2002,
abstract = {We investigate the existence of solutions of the Dirichlet problem for the differential inclusion $0 ∈ Δ x(y) + ∂_\{x\}G(y,x(y))$ for a.e. y ∈ Ω, which is a generalized Euler-Lagrange equation for the functional $J(x) = ∫_\{Ω\}\{ 1/2|∇x(y)|² - G(y,x(y))\}dy$. We develop a duality theory and formulate the variational principle for this problem. As a consequence of duality, we derive the variational principle for minimizing sequences of J. We consider the case when G is subquadratic at infinity.},
author = {Aleksandra Orpel},
journal = {Annales Polonici Mathematici},
keywords = {Dirichlet problem; duality; variational principle; Euler-Lagrange equation},
language = {eng},
number = {2},
pages = {131-140},
title = {The Dirichlet problem with sublinear nonlinearities},
url = {http://eudml.org/doc/280968},
volume = {78},
year = {2002},
}

TY - JOUR
AU - Aleksandra Orpel
TI - The Dirichlet problem with sublinear nonlinearities
JO - Annales Polonici Mathematici
PY - 2002
VL - 78
IS - 2
SP - 131
EP - 140
AB - We investigate the existence of solutions of the Dirichlet problem for the differential inclusion $0 ∈ Δ x(y) + ∂_{x}G(y,x(y))$ for a.e. y ∈ Ω, which is a generalized Euler-Lagrange equation for the functional $J(x) = ∫_{Ω}{ 1/2|∇x(y)|² - G(y,x(y))}dy$. We develop a duality theory and formulate the variational principle for this problem. As a consequence of duality, we derive the variational principle for minimizing sequences of J. We consider the case when G is subquadratic at infinity.
LA - eng
KW - Dirichlet problem; duality; variational principle; Euler-Lagrange equation
UR - http://eudml.org/doc/280968
ER -