[00634] Bifurcation curves for semipositone problem with Minkowski-curvature operator

Session Time & Room : 5D (Aug.25, 15:30-17:10) @G502

Type : Contributed Talk

Abstract : We study the shape of bifurcation curve of positive solutions for the semipositone Minkowski-curvature problem $-\left( u^{\prime }/\sqrt{1-{u^{\prime }}^{2}}\right) ^{\prime }=\lambda f(u),$ in $\left( -L,L\right) $, and $u(-L)=u(L)=0,$ where $\lambda ,L>0$ and $\left( \beta -u\right) f(u)<0$ for $u>0$. We prove that if $f$ is either convex or concave, then the bifurcation curve is C-shaped.