Entire solutions of the nonlinear eigenvalue logistic problem with sign-changing potential and absorbtion
Dinu, Teodora Liliana
arXiv, 0511156 / Harvested from arXiv
Text on arXiv
We are concerned with positive solutions decaying to zero at infinity for the logistic equation $-\Delta u=\lambda (V(x)u-f(u))$ in $\RR^N$, where $V(x)$ is a variable potential that may change sign, $\lambda$ is a real parameter, and $f$ is an absorbtion term such that the mapping $f(t)/t$ is increasing in $(0,\infty)$. We prove that there exists a bifurcation non-negative number $\Lambda$ such that the above problem has exactly one solution if $\lambda >\Lambda$, but no such a solution exists provided $\lambda\leq\Lambda$.
Publié le : 2005-11-07
Classification:  Mathematics - Analysis of PDEs,  Mathematical Physics,  35A05, 35B40, 35J60, 37K50, 92D25 
@article{0511156,
     author = {Dinu, Teodora Liliana},
     title = {Entire solutions of the nonlinear eigenvalue logistic problem with
  sign-changing potential and absorbtion},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511156}
}

Dinu, Teodora Liliana. Entire solutions of the nonlinear eigenvalue logistic problem with
  sign-changing potential and absorbtion. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511156/