Characterization of Essential Stability in Lower Pseudocontinuous Optimization Problems

Characterization of essential stability of minimum solutions for a class of optimization problems with boundedness and lower pseudocontinuity on a compact metric space is given. It shows that any optimization problem considered here has one essential component(resp. one essential minimum solution) if and only if its minimum solution set is connected(resp. singleton) and that those optimization problems which have a unique minimum solution form a residual set(however, which need not to be dense).