A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative,...A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.展开更多
We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tenso...We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, Btensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP;and hence, they are very easy to calculate.展开更多
In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity) conditions for a functional of two variables ψ（x,y) in the general variational i...In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity) conditions for a functional of two variables ψ（x,y) in the general variational inequalities.Last,we show a proof of non-topological degree meth-od of acute principle about monotone operator as an application of these results.展开更多
In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities...In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.展开更多
基金Supported by Grant No.201/01/1451 of the Grant Agency of Czech Republicthe Council of Czech Government J14/98:153100011
文摘A new upper and lower solution theory is presented for the second order problem （G＇（y））＇＋ f（t, y） = 0 on finite and infinite intervals. The theory on finite intervals is based on a Leray-Schauder alternative, where as the theory on infinite intervals is based on results on the finite interval and a diagonalization process.
文摘We introduce a class of structured tensors, called generalized row strictly diagonally dominant tensors, and discuss some relationships between it and several classes of structured tensors, including nonnegative tensors, Btensors, and strictly copositive tensors. In particular, we give estimations on upper and lower bounds of solutions to the tensor complementarity problem (TCP) when the involved tensor is a generalized row strictly diagonally dominant tensor with all positive diagonal entries. The main advantage of the results obtained in this paper is that both bounds we obtained depend only on the tensor and constant vector involved in the TCP;and hence, they are very easy to calculate.
文摘In this paper,applying the concept of generalized KKM map,we study problems of variational inequalities.We weaken convexity(concavity) conditions for a functional of two variables ψ（x,y) in the general variational inequalities.Last,we show a proof of non-topological degree meth-od of acute principle about monotone operator as an application of these results.
文摘In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.
