# Bifurcations for a problem with jumping nonlinearities

Mathematica Bohemica (2002)

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

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topKárná, 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 -

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