Unilateral Global Interval Bifurcation for the Hessian Equation and Its Applications

Abstract EN

In this paper, we establish a unilateral global bifurcation result from the interval for the k-Hessian equations with nondifferentiable nonlinearity.

By applying the above result, we shall prove the existence of the principal half-eigenvalues for the half quasilinear problems.

Furthermore, we shall determine the interval of γ, in which there exist one-sign solutions for the following k-Hessian equations: SkD2u=αx−u+k+βx−u−k+γaxfu, in B,ux=0, on ∂B.