Geodesic
Bifurcations for a problem with jumping nonlinearities
Mathematica Bohemica, Tome 127 (2002) no. 3, pp. 481-496

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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 $\lambda ^{(1)}, \lambda ^{(2)}$.
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 $\lambda ^{(1)}, \lambda ^{(2)}$.
DOI : 10.21136/MB.2002.134065
Classification : 35B32, 35J25, 35J60, 35J65
Keywords: nonlinearizable elliptic equations; jumping nonlinearities; global bifurcation; half-eigenvalue 
Kárná, Lucie; Kučera, Milan. Bifurcations for a problem with jumping nonlinearities. Mathematica Bohemica, Tome 127 (2002) no. 3, pp. 481-496. doi: 10.21136/MB.2002.134065
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