Positive Solutions of Nonlinear Elliptic Equations with Nonlinear Boundary Conditions

This paper discusses bifurcation from interval for the elliptic eigenvalue problems with nonlinear boundary conditions and studies the behavior of the bifurcation components.

Bifurcation from Interval and Positive Solutions of a Nonlinear Second-Order Dynamic Boundary Value Problem on Time Scales

Let𝕋be a time scale with0,T∈𝕋. We give a global description of the branches of positive solutions to the nonlinear boundary value problem of second-order dynamic equation on a time scale𝕋,uΔΔ(t)+f(t,uσ(t))=0, t∈[0,T]𝕋, u(0)=u(σ2(T))=0, which is not necessarily linearizable. Our approaches are based on topological degree theory and global bifurcation techniques.