Upper and lower bounds for higher order eigenvalues of some semilinear elliptic equations

Precise Asymptotics for Bifurcation Curve of Nonlinear Ordinary Differential Equation

“…As far as the author knows, however, the exact solution u α (t) of the equation in Theorem 1 is not known, although it is quite simple, and it also seems impossible to obtain the explicit formula for λ(α) as (5). From this point of view, one of the standard approaches for the better understanding of the global structure of λ(α) is to establish precise asymptotic expansion formula for λ(α) as α → ∞.…”

“…Nonlinear eigenvalue and bifurcation problems have been one of the main topics in the study of nonlinear equations, and many authors have investigated the global behavior of bifurcation diagrams intensively. We refer to [2][3][4][5][6][7] and the references therein.…”

Global and Local Structures of Bifurcation Curves of ODE with Nonlinear Diffusion

“…Bifurcation problems have a long history and there are so many results concerning the asymptotic properties of bifurcation diagrams. We refer to [1][2][3][4][5][6][7][8] and the references therein. Moreover, bifurcation problems with nonlinear diffusion have been proposed in the field of population biology, and several model equations of logistic type have been considered.…”

Asymptotic Behavior of the Bifurcation Diagrams for Semilinear Problems with Application to Inverse Bifurcation Problems

“…Nonlinear elliptic eigenvalue problems have been studied by many authors. We refer to [2][3][4][5][6][7][8] and the references therein. Among other things, (1)- (3) have been investigated by many authors.…”