In this paper,we are concerned with Cauchy problem for the multi-dimensional(N > 3)non-isentropic full compressible magnetohydrodynamic equations.We prove the existence and uniqueness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces.Our method is mainly based on the uniform estimates in Besov spaces for the proper linearized system with convective terms.
We discuss Ky Fan's theorem and the variational inequality problem for discontinuous mappings f in a Banach space X. The main tools of analysis are the variational characterizations of the metric projection operator and the order-theoretic fixed point theory. Moreover, we derive some properties of the metric projection operator in Banach spaces. As applications of our best approximation theorems, three fixed point theorems for non-self maps are established and proved under some conditions. Our results are generalizations and improvements of various recent results obtained by many authors.
We study the existence of positive solutions to boundary value problems for onedimensional p-Laplacian under some conditions about the first eigenvalues corresponding to the relevant operators by the fixed point theory.The main difficulties are the computation of fixed point index and the subadditivity for positively 1-homogeneous operator.
