Necessary Conditions of Weak Efficiency for a Class of Nondifferentiable Vector Optimization Problems
the Kuhn-Tucker type necessary conditions for weak efficiency are given for a class of the problem of minimizing a vector function of which each component is the sum of a differentiable function and a convex function subject to a set of differentiable nonlinear inequalities on an open subset X of R~n,under the weaker constraint qualification.The results obtained improve and extend some of the existing results in the literature.
In this paper, we study the sharp energy criteria of blow-up and global existence for the nonlinear Klein-Gordon equation by the sharp Gagliardo-Nirebergy-Sobolev inequality.