After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some ...After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.展开更多
文摘After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.
