In this paper to the theorem of the “Mountain Impasse” Type given by K.Tintarev,we consider the condition: the state of that “for every p∈Φ ∞, max ξ∈K G(p(ξ)) is attained at some point in K\K *” is relaxed f...In this paper to the theorem of the “Mountain Impasse” Type given by K.Tintarev,we consider the condition: the state of that “for every p∈Φ ∞, max ξ∈K G(p(ξ)) is attained at some point in K\K *” is relaxed from c(R)>c 0.展开更多
Motivated to obtain the second critical point of a nonlinear differential equation, which is expressed by derivatives of convex functional defined on a Banach space, an estimate with is given to see the relation ...Motivated to obtain the second critical point of a nonlinear differential equation, which is expressed by derivatives of convex functional defined on a Banach space, an estimate with is given to see the relation between f<sup>-1</sup>(0) and g<sup>-1</sup>(0). And both the Fréchet differentiability and the continuity of Fréchet derivative of every convex functional defined on an open subset of a Banach space are shown.展开更多
文摘In this paper to the theorem of the “Mountain Impasse” Type given by K.Tintarev,we consider the condition: the state of that “for every p∈Φ ∞, max ξ∈K G(p(ξ)) is attained at some point in K\K *” is relaxed from c(R)>c 0.
文摘Motivated to obtain the second critical point of a nonlinear differential equation, which is expressed by derivatives of convex functional defined on a Banach space, an estimate with is given to see the relation between f<sup>-1</sup>(0) and g<sup>-1</sup>(0). And both the Fréchet differentiability and the continuity of Fréchet derivative of every convex functional defined on an open subset of a Banach space are shown.
