caa a22 4500 605496382 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10231-014-0404-8 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0404-8 Miyamoto Yasuhito Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914, Tokyo, Japan aut Classification of bifurcation diagrams for elliptic equations with exponential growth in a ball [Elektronische Daten] [Yasuhito Miyamoto] Let $$B\subset \mathbb {R}^N$$ B ⊂ R N , $$N\ge 3$$ N ≥ 3 , be the unit ball. We study the global bifurcation diagram of the solutions of $$\begin{aligned} {\left\{ \begin{array}{ll} \Delta u+\lambda f(u)=0 &{}\quad \text {in}\ B,\\ u=0 &{} \quad \text {on}\ \partial B,\\ u>0 &{} \quad \text {in}\ B, \end{array}\right. } \end{aligned}$$ Δ u + λ f ( u ) = 0 in B , u = 0 on ∂ B , u > 0 in B , where $$f(u)=e^u+g(u)$$ f ( u ) = e u + g ( u ) and $$g(u)$$ g ( u ) is a lower order term. The solution set is a curve $$\mathcal {C}$$ C parametrized by the $$L^{\infty }$$ L ∞ -norm of the solution. We show that this problem has the singular solution $$(\lambda ^*,u^*)$$ ( λ ∗ , u ∗ ) and that the curve $$\mathcal {C}$$ C has infinitely many turning points around $$\lambda ^*$$ λ ∗ if $$3\le N\le 9$$ 3 ≤ N ≤ 9 . We show that under a certain condition on $$g$$ g , the curve $$\mathcal {C}$$ C has no turning point if $$N\ge 10$$ N ≥ 10 . We also study the Morse index of $$u^*$$ u ∗ . Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Bifurcation diagram nationallicence Exponential growth nationallicence Intersection number nationallicence Elliptic Dirichlet problem nationallicence Singular solution nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 931-952 0373-3114 194:4<931 2015 194 10231 https://doi.org/10.1007/s10231-014-0404-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0404-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Miyamoto Yasuhito Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, 153-8914, Tokyo, Japan aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/4(2015-08-01), 931-952 0373-3114 194:4<931 2015 194 10231