解析学火曜セミナー

過去の記録 ~04/13次回の予定今後の予定 04/14~

開催情報 火曜日 16:00~17:30 数理科学研究科棟(駒場) 156号室
担当者 石毛 和弘, 坂井 秀隆, 伊藤 健一
セミナーURL https://www.ms.u-tokyo.ac.jp/seminar/analysis/

2023年07月11日(火)

16:00-17:30   数理科学研究科棟(駒場) 123号室
対面・オンラインハイブリッド開催,通常とは場所が異なります
Julian López-Gómez 氏 (Complutense University of Madrid)
Nodal solutions for a class of degenerate BVP’s (English)
[ 講演概要 ]
In this talk we characterize the existence of nodal solutions for a generalized class of one-dimensional diffusive logistic type equations, including
\[−u''=\lambda u−a(x)u^3,\quad x∈[0,L],\]
under the boundary conditions $u(0)=u(L)=0$, where $\lambda$ is regarded as a bifurcation parameter, and the non-negative weight function $a(x)$ vanishes on some subinterval
\[ [\alpha,\beta]\subset (0,L)\]
with $\alpha<\beta$.

At a later stage, the general case when $a(x)$ vanishes on finitely many subintervals with the same length is analyzed. Finally, we construct some examples with classical non-degenerate weights, with $a(x)>0$ for all $x∈[0,L]$, where the BVP has an arbitrarily large number of solutions with one node in $(0,L)$. These are the first examples of this nature constructed in the literature.

References:

P. Cubillos, J. López-Gómez and A. Tellini, Multiplicity of nodal solutions in classical non-degenerate logistic equations, El. Res. Archive 30 (2022), 898—928.

J. López-Gómez, M. Molina-Meyer and P. H. Rabinowitz, Global bifurcation diagrams of one-node solutions on a class of degenerate boundary value problems, Disc. Cont. Dyn. Syst. B 22 (2017), 923—946.

J. López-Gómez and P. H. Rabinowitz, Nodal solutions for a class of degenerate one dimensional BVP’s, Top. Meth. Nonl. Anal. 49 (2017), 359—376.

J. López-Gómez and P. H. Rabinowitz, The estructure of the set of 1-node solutions for a class of degenerate BVP’s, J. Differential Equations 268 (2020), 4691—4732.

P. H. Rabinowitz, A note on a anonlinear eigenvalue problem for a class of differential equations, J. Differential Equations 9 (1971), 536—548.
[ 参考URL ]
https://forms.gle/S3VgMSWg9wUP69cY6