The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and b...The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.展开更多
This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequali...This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and the method of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solu- tions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.展开更多
In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate t...In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10971194)the Zhejiang Provincial Natural Science Foundation of China (Nos. Y7080008, R6090109)the Zhejiang Innovation Project (No. T200905)
文摘The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.
文摘This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms. The authors use skills of inequality estimation and the method of regularization to construct a sequence of approximation solutions, hence obtain the global existence of solutions to a regularized system. Then the global existence of solu- tions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process. The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.
基金Supported by the National Natural Science Foundation of China(12101452,12071229,11771218)。
文摘In this paper,we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p-Laplacian systems.By virtue of this method,we investigate the qualitative properties of positive solutions for the following Schrodinger system with fractional p-Laplacian{(-△)^(s)_(p)u+au^(p-1)=f(u,v),(-△)^(t)_(p)v+bv(p-1)=g(u,v),where 0<s,t<1 and 2<p<∞.We obtain the radial symmetry in the unit ball or the whole space R^(N)(N≥2),the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g,respectively.
