@article{Shibata_2022, title={Asymptotic behavior of bifurcation curve of nonlinear eigenvalue problem with logarithmic nonlinearity}, volume={60}, url={https://apcz.umk.pl/TMNA/article/view/39287}, DOI={10.12775/TMNA.2021.040}, abstractNote={We study the following nonlinear eigenvalue problem $$ -uā€™ā€™(t) = \lambda u(t)^p\log(1+u(t)), \quad u(t) > 0, \quad t \in I := (-1,1), \quad u(\pm 1) = 0, $$% where $p \ge 0$ is a given constant and $\lambda > 0$ is a parameter. It is known that, for any given $\alpha > 0$, there exists a unique classical solution pair $(\lambda(\alpha), u_\alpha)$ with $\alpha = \Vert u_\alpha\Vert_\infty$. We establish the asymptotic formulas for the bifurcation curves $\lambda(\alpha)$ and the shape of solution $u_\alpha$ as $\alpha \to \infty$ and $\alpha \to 0$.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Shibata, Tetsutaro}, year={2022}, month={Jul.}, pages={99ā€“110} }