The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are gi...The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations.展开更多
Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler c...Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler conjectured that the equation +μsin+x=0 has infinite number of limit cycles. Then H. S. Hochstadt and B. Stephan, R. N. D’Heedene and others proved that this equation has at least n limit cycles in the interval |x|<(n+1)π for specified parameter μ. In 1980, Professor Zhang Zhifen proved that this equation has exact n limit cycles in the interval |x|<(n+1)π for any nonzero parameter μ, and thus pushed the related work forward greatly. In this paper, we shall prove that the Liénard’s equation has exact n limit cycles in a finite interval under a class of very general condition.展开更多
In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the ...In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.展开更多
This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions ar...This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.展开更多
Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a ration...Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a rational function on the Riemann sphere with branch data ■ if and only if max(m1,...,ml)<d/GCD(a1,...,ap,b1,...bq),As an application,we give a new class of branch data which can be realized by Belyi functions on the Riemann sphere.展开更多
文摘The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations.
文摘Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler conjectured that the equation +μsin+x=0 has infinite number of limit cycles. Then H. S. Hochstadt and B. Stephan, R. N. D’Heedene and others proved that this equation has at least n limit cycles in the interval |x|<(n+1)π for specified parameter μ. In 1980, Professor Zhang Zhifen proved that this equation has exact n limit cycles in the interval |x|<(n+1)π for any nonzero parameter μ, and thus pushed the related work forward greatly. In this paper, we shall prove that the Liénard’s equation has exact n limit cycles in a finite interval under a class of very general condition.
基金The first author was supported by the Guangxi Natural Science Foundation of China(Grant No.2021GXNSFFA196004)National Natural Science Foundation of China(Grant No.12001478)+4 种基金Horizon 2020 of the European Union(Grant No.823731 CONMECH)National Science Center of Poland(Grant No.2017/25/N/ST1/00611)The second author was supported by National Science Foundation of USA(Grant No.DMS 1720067)The third author was supported by the National Science Center of Poland(Grant No.2021/41/B/ST1/01636)the Ministry of Science and Higher Education of Poland(Grant Nos.4004/GGPJII/H2020/2018/0 and 440328/PnH2/2019)。
文摘In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential.
基金Institute for Research in Fundamental Sciences(No.96580048).
文摘This paper deals with approximate weak minimal solutions of set-valued optimization problems under vector and set optimality criteria.The relationships between various concepts of approximate weak minimal solutions are investigated.Some topological properties and existence theorems of these solutions are given.It is shown that for set-valued optimization problems with upper(outer)cone-semicontinuous objective values or closed objective maps the approximate weak minimal and strictly approximate lower weak minimal solution sets are closed.By using the polar cone and two scalarization processes,some necessary and sufficient optimality conditions in the sense of vector and set criteria are provided.
基金supported in part by the National Natural Science Foundation of China(grant no.11426236)The second author was supported in part by the National Natural Science Foundation of China(grant nos.11571330 and 11971450)the Fundamental Research Funds for the Central Universities.
文摘Let d be a positive integer and八be a collection of partitions of d of the form(a1,...,ap),(b1,...,bq),(m1+1,1,...,1),...,(m1+1,1,...,1),where(m1,...,ml)is a partition of p+g-2>0.We prove that there exists a rational function on the Riemann sphere with branch data ■ if and only if max(m1,...,ml)<d/GCD(a1,...,ap,b1,...bq),As an application,we give a new class of branch data which can be realized by Belyi functions on the Riemann sphere.