This paper concerns the exact multiplicity of one-sign solutions of a class of quasilinear elliptic eigenvalue problems with asymptotical nonlinearity at 0 and ∞. The proofs of our main results are based upon bifurca...This paper concerns the exact multiplicity of one-sign solutions of a class of quasilinear elliptic eigenvalue problems with asymptotical nonlinearity at 0 and ∞. The proofs of our main results are based upon bifurcation techniques and stability analysis.展开更多
By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=...By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=λNH,with a 0-Dirichlet boundary condition on the unit ball.According to the behavior of H near 0,we obtain the global structure of sign-changing radial spacelike graphs for this problem.展开更多
This paper is concerned with the existence of solutions to a class of p（x）-Kirchhoff-type systems under Neumann boundary condition. By Ekeland Variational Principle and the theory of the variable exponent Sobolev sp...This paper is concerned with the existence of solutions to a class of p（x）-Kirchhoff-type systems under Neumann boundary condition. By Ekeland Variational Principle and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence of solutions for the problem. Since the Poincare＇s inequality does not hold in the space W1,p（x）（Ω）, we shall prove the Poincare-Wirtinger＇s inequality in a subspace of W1,p（x）（Ω）.展开更多
An experimental study is conducted to describe rate-dependent shear strength in a submerged granular medium to understand the mystery of submarine landslides with extremely small slide angles and long run-out distance...An experimental study is conducted to describe rate-dependent shear strength in a submerged granular medium to understand the mystery of submarine landslides with extremely small slide angles and long run-out distances.The experimental apparatus allows a long-span shear strain rate,■,for five orders of magnitude from 10^(-4)to 10^(1)s^(-1).It is observed that(a)submerged sand under higher shear tend to have bigger yield strength;this positive response of rate effect is significantly affected by the magnitudes of shear strain rates.(b)the residual strength of soil is clearly affected negatively by shear strain rate,decreasing as shear strain rate increases;even small variations under lower rate cause notable differences in residual strength,indicating a novel weaking rate-dependent.The yield strength and residual strength are corresponding to the shear state of soil.Hence,it is enough experimentally to explain that as long as the submarine mass flow speeds up,the slope sliding can be kept by only a small amount of force along the slide direction,which can be calculated as the gravity component even with a small slide angle.展开更多
We establish the unilateral global bifurcation result for the following nonlinear operator equation u=L(λ)u + H(λ, u),(λ, u)∈ Rm×X where m is a positive integer, X is a Banach space, L(·) is a positively...We establish the unilateral global bifurcation result for the following nonlinear operator equation u=L(λ)u + H(λ, u),(λ, u)∈ Rm×X where m is a positive integer, X is a Banach space, L(·) is a positively homogeneous completely continuous operator and H:R^m×X → X is completely continuous with H=o (||u||) near u=0 uniformly on bounded λ sets.展开更多
基金Supported by the National Natural Science Foundation of China (Grant Nos.1126105211101335)
文摘This paper concerns the exact multiplicity of one-sign solutions of a class of quasilinear elliptic eigenvalue problems with asymptotical nonlinearity at 0 and ∞. The proofs of our main results are based upon bifurcation techniques and stability analysis.
基金Research supported by NNSF of China(11871129)Xinghai Youqing funds from Dalian University of Technology+1 种基金NSF of Liaoning Province(2019-MS-109)HSSF of Chinese Ministry of Education(20YJA790049).
文摘By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=λNH,with a 0-Dirichlet boundary condition on the unit ball.According to the behavior of H near 0,we obtain the global structure of sign-changing radial spacelike graphs for this problem.
基金Supported by the National Natural Science Foundation of China(Grant No.11261052)
文摘This paper is concerned with the existence of solutions to a class of p（x）-Kirchhoff-type systems under Neumann boundary condition. By Ekeland Variational Principle and the theory of the variable exponent Sobolev spaces, we establish conditions ensuring the existence of solutions for the problem. Since the Poincare＇s inequality does not hold in the space W1,p（x）（Ω）, we shall prove the Poincare-Wirtinger＇s inequality in a subspace of W1,p（x）（Ω）.
基金financially supported by the National Natural Science Foundation of China(Nos.42120104008,41831291,42002273)the Fundamental Research Funds for the Central Universities(No.22120210143)。
文摘An experimental study is conducted to describe rate-dependent shear strength in a submerged granular medium to understand the mystery of submarine landslides with extremely small slide angles and long run-out distances.The experimental apparatus allows a long-span shear strain rate,■,for five orders of magnitude from 10^(-4)to 10^(1)s^(-1).It is observed that(a)submerged sand under higher shear tend to have bigger yield strength;this positive response of rate effect is significantly affected by the magnitudes of shear strain rates.(b)the residual strength of soil is clearly affected negatively by shear strain rate,decreasing as shear strain rate increases;even small variations under lower rate cause notable differences in residual strength,indicating a novel weaking rate-dependent.The yield strength and residual strength are corresponding to the shear state of soil.Hence,it is enough experimentally to explain that as long as the submarine mass flow speeds up,the slope sliding can be kept by only a small amount of force along the slide direction,which can be calculated as the gravity component even with a small slide angle.
基金supported by National Natural Science Foundation of China(11871129)
文摘We establish the unilateral global bifurcation result for the following nonlinear operator equation u=L(λ)u + H(λ, u),(λ, u)∈ Rm×X where m is a positive integer, X is a Banach space, L(·) is a positively homogeneous completely continuous operator and H:R^m×X → X is completely continuous with H=o (||u||) near u=0 uniformly on bounded λ sets.
