The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we est...The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we establish the existence of infinitely many weak solutions for this problem.展开更多
We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ...We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.展开更多
A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account...A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities(Grant No.31920180041)the Fund for Talent Introduction of Northwest Minzu University(Grant No.xbmuyjrc201907)。
文摘The purpose of this paper is to investigate a nonlocal Dirichlet problem with(p(x),q(x))-Laplacian-like operator originated from a capillary phenomena.Using the variational methods and the critical point theory,we establish the existence of infinitely many weak solutions for this problem.
基金Supported by the Scientific Research Funds for the Ningxia Universities(Grant No.NGY2015141)
文摘We establish the existence of positive periodic solutions of the second-order singular coupled systems{x′′＋ p_1（t）x′＋ q_1（t）x = f_1（t, y（t）） ＋ c_1（t）,y′′＋ p_2（t）y′＋ q_2（t）y = f_2（t, x（t）） ＋ c_2（t）,where pi, qi, ci ∈ C（R/T Z; R）, i = 1, 2; f_1, f_2 ∈ C（R/T Z ×（0, ∞）, R） and may be singular near the zero. The proof relies on Schauder＇s fixed point theorem and anti-maximum principle.Our main results generalize and improve those available in the literature.
文摘A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.
