For domains of first kind [7,13] we describe the qualitative behavior global bifurcation diagram unbounded branch solutions Gel'fand problem crossing origin. At least to our knowledge this is result about exact monotonicity non-minimal which not just concerned with radial [28] and/or symmetric [23]. Toward goal parametrize by $L^{\infty}(\Omega)$-norm but energy associated mean field problem. T...

In this paper we consider a class of symbols of infinite order and develop a global calculus for the related pseudodifferential operators in the functional frame of the Gelfand-Shilov spaces of type S. As an application, we construct a parametrix for the Cauchy problem associated to an operator with principal part Dm t and lower order terms given by SGoperators, cf. Introduction. We do not assu...