By discussing the properties of a linear cooperative system, the necessary and sufficient conditions for the existence of positive solutions of an elliptic cooperative system in terms of the principal eigenvalue of th...By discussing the properties of a linear cooperative system, the necessary and sufficient conditions for the existence of positive solutions of an elliptic cooperative system in terms of the principal eigenvalue of the associated linear system are established, and some local stability results for the positive solutions are also obtained.展开更多
This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient ...This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.展开更多
Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegati...Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.展开更多
Concepts of g-supersolution, g-manrtingale, g-supermartingale are introduced, which are related to BSDE with Brownian motion and Poisson point process. A strict comparison theorem, monotonic limit theorem related to t...Concepts of g-supersolution, g-manrtingale, g-supermartingale are introduced, which are related to BSDE with Brownian motion and Poisson point process. A strict comparison theorem, monotonic limit theorem related to this type of BSDE are also discussed. As an application of these results, a nonlinear Doob-Meyer decomposition theorem is obtained.展开更多
The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and...The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.展开更多
In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz＇ya term：-Δu-λ u/｜y｜2 = （｜u｜pt-1u）/｜y｜t ＋ μf（x）, x∈ Ω,where ...In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz＇ya term：-Δu-λ u/｜y｜2 = （｜u｜pt-1u）/｜y｜t ＋ μf（x）, x∈ Ω,where Ω is a bounded domain in RN（N ≥ 2）, 0 ∈ Ω, x = （y, z） ∈ Rk ×RN-k and pt = （N＋2-2t）/（N-2） （0 ≤ t ≤ 2）. For f（x） ∈ C1（Ω）／{0}, we show that there exists a constant μ＊ 〉0 such that the problem possesses at least two positive solutions if μ ∈ （0, μ＊） and at least one positive solution if μ = μ＊. Furthermore, there are no positive solutions if μ ∈ （μ＊,＋∞）.展开更多
This paper first proves the following equations△u-m￣2u+f(x,u)=0, x(R￣n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
基金Project supported by the National Natural Science Foundation of China(10071048) Liu Hui Center for Applied Mathematics,Nankai University and Tianjin University
文摘By discussing the properties of a linear cooperative system, the necessary and sufficient conditions for the existence of positive solutions of an elliptic cooperative system in terms of the principal eigenvalue of the associated linear system are established, and some local stability results for the positive solutions are also obtained.
文摘This paper deals with the existence and nonexistence of global positive solution of the following equation:where p, q, m, α are parameters with is a bounded domain with Ω smooth enough, The necessary and sufficient conditions for the global existence of solution are obtained.
文摘Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.
文摘Concepts of g-supersolution, g-manrtingale, g-supermartingale are introduced, which are related to BSDE with Brownian motion and Poisson point process. A strict comparison theorem, monotonic limit theorem related to this type of BSDE are also discussed. As an application of these results, a nonlinear Doob-Meyer decomposition theorem is obtained.
基金Partially supported by the project-sponsored by SRF for ROCS, SEM
文摘The author studies semilinear parabolic equations with initial and periodic boundary value conditions. In the presence of non-well-ordered sub- and super-solutions： ＂subsolution ≮ supersolution＇, the existence and stability/instability of equilibrium solutions are obtained.
基金Supported by NSFC(Grant No.11301204)the Ph D specialized grant of the Ministry of Education of China(Grant No.20110144110001)the excellent doctorial dissertation cultivation grant from Central China Normal University(Grant No.2013YBZD15)
文摘In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz＇ya term：-Δu-λ u/｜y｜2 = （｜u｜pt-1u）/｜y｜t ＋ μf（x）, x∈ Ω,where Ω is a bounded domain in RN（N ≥ 2）, 0 ∈ Ω, x = （y, z） ∈ Rk ×RN-k and pt = （N＋2-2t）/（N-2） （0 ≤ t ≤ 2）. For f（x） ∈ C1（Ω）／{0}, we show that there exists a constant μ＊ 〉0 such that the problem possesses at least two positive solutions if μ ∈ （0, μ＊） and at least one positive solution if μ = μ＊. Furthermore, there are no positive solutions if μ ∈ （μ＊,＋∞）.
文摘This paper first proves the following equations△u-m￣2u+f(x,u)=0, x(R￣n,n≥3 m>0 existence of decaying positive entire solution, then emphatically, proves this solution'suniqueness.
