The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their ch...The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their characterizations for the boundedness are not complete.In this paper,the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^(p)_(α)to _(Dβ)^(q)(-1<α,βand 0<p<q<∞),which essentially complete their works.Furthermore,the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.展开更多
In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower soluti...In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.展开更多
Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solution...Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.展开更多
基金supported by the National Natural Science Foundation of China(No.11801094)。
文摘The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their characterizations for the boundedness are not complete.In this paper,the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^(p)_(α)to _(Dβ)^(q)(-1<α,βand 0<p<q<∞),which essentially complete their works.Furthermore,the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.
文摘In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.
文摘Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.
