Under the democratic systems of government instilled in many sovereign states, the party in government maintains a constitutional right to call an early election. Whereas the constitution states that there is a maximum period between elections, early elections are frequently called. This right to call an early election gives the government a control to maximize its remaining period in power. We find the optimal control for the government by locating an exercise boundary, which indicates whether or not a premature election should be called. This problem draws upon the methods of optimal stopping and stochastic control.

No abstract

Abstract.We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.2000 Mathematics Subject Classification. 47J15, 35J60, 35J65, 47J10.

No abstract

In this paper we establish the existence of multiple solutions for a semilinear elliptic equation with competing convex and concave nonlinearities. With either a subcritical or critical exponent in the nonlinearity, the existence of solutions is determined with critical point theorems based on the symmetric mountain pass theorem.