In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above res...In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above result,we shall prove the existence of one-sign solutions to the following problem{−div(√∇v 1−|∇v|^(2))=α(x)v^(+)+β(x)v^(−)+λa(x)f(v),in B_(R)(0),v(x)=0,on∂B_(R)(0),whereλ≠=0 is a parameter,R is a positive constant and BR(0)={x∈RN:|x|<R}is the standard open ball in the Euclidean space RN(N≥1)which is centered at the origin and has radius R.v^(+)=max{v,0},v−=−min{v,0},a(x)∈C(BR(0),(0,+∞)),α(x),β(x)∈C(BR(0)),a(x),α(x)andβ(x)are radially symmetric with respect to x;f∈C(R,R),sf(s)>0 for s≠=0,and f_(0)∈[0,∞],where f0=lim_(|s|)→0 f(s)/s.We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.We also study the asymptotic behaviors of positive radial solutions asλ→+∞.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
基金Supported by the`Kaiwu'Innovation Team Support Project of Lanzhou Institute of Technology(2018KW-03),the NSFC(11561038).
文摘In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above result,we shall prove the existence of one-sign solutions to the following problem{−div(√∇v 1−|∇v|^(2))=α(x)v^(+)+β(x)v^(−)+λa(x)f(v),in B_(R)(0),v(x)=0,on∂B_(R)(0),whereλ≠=0 is a parameter,R is a positive constant and BR(0)={x∈RN:|x|<R}is the standard open ball in the Euclidean space RN(N≥1)which is centered at the origin and has radius R.v^(+)=max{v,0},v−=−min{v,0},a(x)∈C(BR(0),(0,+∞)),α(x),β(x)∈C(BR(0)),a(x),α(x)andβ(x)are radially symmetric with respect to x;f∈C(R,R),sf(s)>0 for s≠=0,and f_(0)∈[0,∞],where f0=lim_(|s|)→0 f(s)/s.We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.We also study the asymptotic behaviors of positive radial solutions asλ→+∞.
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.
