A nonlocal elliptic equation in a bounded domain

Piotr Fijałkowski, Bogdan Przeradzki, and Robert Stańczy. "A nonlocal elliptic equation in a bounded domain." Banach Center Publications 66.1 (2004): 127-133. <http://eudml.org/doc/281692>.

@article{PiotrFijałkowski2004,
abstract = {The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $-∑_\{i,j=1\}^\{n\} D_i(a_\{ij\}D_ju) = f(u,∫_\{Ω\}g(u^p))$, in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.},
author = {Piotr Fijałkowski, Bogdan Przeradzki, Robert Stańczy},
journal = {Banach Center Publications},
keywords = {elliptic boundary value problem; nonlocal equation; cone; positive solution; multiple solutions},
language = {eng},
number = {1},
pages = {127-133},
title = {A nonlocal elliptic equation in a bounded domain},
url = {http://eudml.org/doc/281692},
volume = {66},
year = {2004},
}

TY - JOUR
AU - Piotr Fijałkowski
AU - Bogdan Przeradzki
AU - Robert Stańczy
TI - A nonlocal elliptic equation in a bounded domain
JO - Banach Center Publications
PY - 2004
VL - 66
IS - 1
SP - 127
EP - 133
AB - The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $-∑_{i,j=1}^{n} D_i(a_{ij}D_ju) = f(u,∫_{Ω}g(u^p))$, in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.
LA - eng
KW - elliptic boundary value problem; nonlocal equation; cone; positive solution; multiple solutions
UR - http://eudml.org/doc/281692
ER -