Bifurcations for a problem with jumping nonlinearities

Lucie Kárná; Milan Kučera

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 3, page 481-496
  • ISSN: 0862-7959

Abstract

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A bifurcation problem for the equation Δ u + λ u - α u + + β u - + g ( λ , u ) = 0 in a bounded domain in N with mixed boundary conditions, given nonnegative functions α , β ∈ L ∞ and a small perturbation g is considered. The existence of a global bifurcation between two given simple eigenvalues λ ( 1 ) , λ ( 2 ) of the Laplacian is proved under some assumptions about the supports of the functions α , β . These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to λ ( 1 ) , λ ( 2 ) .

How to cite

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Kárná, Lucie, and Kučera, Milan. "Bifurcations for a problem with jumping nonlinearities." Mathematica Bohemica 127.3 (2002): 481-496. <http://eudml.org/doc/249045>.

@article{Kárná2002,
abstract = {A bifurcation problem for the equation \[ \Delta u+\lambda u-\alpha u^++\beta u^-+g(\lambda ,u)=0 \] in a bounded domain in $^N$ with mixed boundary conditions, given nonnegative functions $\alpha ,\beta \in L_\infty $ and a small perturbation $g$ is considered. The existence of a global bifurcation between two given simple eigenvalues $\lambda ^\{(1)\},\lambda ^\{(2)\}$ of the Laplacian is proved under some assumptions about the supports of the functions $\alpha ,\beta $. These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to $\lambda ^\{(1)\}, \lambda ^\{(2)\}$.},
author = {Kárná, Lucie, Kučera, Milan},
journal = {Mathematica Bohemica},
keywords = {nonlinearizable elliptic equations; jumping nonlinearities; global bifurcation; half-eigenvalue; nonlinearizable elliptic equations; jumping nonlinearities; global bifurcation; half-eigenvalue},
language = {eng},
number = {3},
pages = {481-496},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Bifurcations for a problem with jumping nonlinearities},
url = {http://eudml.org/doc/249045},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Kárná, Lucie
AU - Kučera, Milan
TI - Bifurcations for a problem with jumping nonlinearities
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 3
SP - 481
EP - 496
AB - A bifurcation problem for the equation \[ \Delta u+\lambda u-\alpha u^++\beta u^-+g(\lambda ,u)=0 \] in a bounded domain in $^N$ with mixed boundary conditions, given nonnegative functions $\alpha ,\beta \in L_\infty $ and a small perturbation $g$ is considered. The existence of a global bifurcation between two given simple eigenvalues $\lambda ^{(1)},\lambda ^{(2)}$ of the Laplacian is proved under some assumptions about the supports of the functions $\alpha ,\beta $. These assumptions are given by the character of the eigenfunctions of the Laplacian corresponding to $\lambda ^{(1)}, \lambda ^{(2)}$.
LA - eng
KW - nonlinearizable elliptic equations; jumping nonlinearities; global bifurcation; half-eigenvalue; nonlinearizable elliptic equations; jumping nonlinearities; global bifurcation; half-eigenvalue
UR - http://eudml.org/doc/249045
ER -

References

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