# A nonlocal elliptic equation in a bounded domain

Piotr Fijałkowski; Bogdan Przeradzki; Robert Stańczy

Banach Center Publications (2004)

- Volume: 66, Issue: 1, page 127-133
- ISSN: 0137-6934

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topPiotr 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 -

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