MULTIPLE ASYMPTOTIC BEHAVIORS OF SOLUTIONS IN THE GENERALIZED VANISHING DISCOUNT PROBLEM

Consider the generalized discounted Hamilton-Jacobi equation lambda a(x)u + H(x, Du) = c(H), where a(x) may vanish or change the signs. Two examples are given in this paper showing that the viscosity solutions of the above equation may not converge as lambda tends to zero.

Automated summary

This paper discusses the convergence of viscosity solutions for the generalized discounted Hamilton-Jacobi equation and provides two examples where the solutions do not converge as lambda tends to zero.