In this paper,we study one-dimensional backward stochastic differential f equation(BSDE),whose deterministic coefficient is Lipschitz in y but only continuous in.If the terminal conditionξhas bounded Malliavin deriva...In this paper,we study one-dimensional backward stochastic differential f equation(BSDE),whose deterministic coefficient is Lipschitz in y but only continuous in.If the terminal conditionξhas bounded Malliavin derivative,we prove some uniqueness results for the BSDE with quadratic and linear growth in,respectively.展开更多
In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0＋ u（t） = f （t, u（t）, c D σ 0＋ u（t））, t...In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0＋ u（t） = f （t, u（t）, c D σ 0＋ u（t））, t ∈ [0, T ], u（0） = αu（η）, u（T ） = βu（η）, where 1 〈 δ 〈 2, 0 〈 σ 〈 1, α, β∈ R, η∈ （0, T ）, αη（1 -β） ＋ （1-α）（T βη） = 0 and c D δ 0＋ , c D σ 0＋ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results.展开更多
基金supported by the National Key R&D Program of China(Grant No.2018YFA0703900)the National Natural Science Foundation of China(Grant Nos.11871309,11371226)+1 种基金the Shandong Provincial Natural Science Foundation(Grant No.ZR2019ZD41)supported by the State Scholarship Fund from the China Scholarship Council(Grant No.201906220089)。
文摘In this paper,we study one-dimensional backward stochastic differential f equation(BSDE),whose deterministic coefficient is Lipschitz in y but only continuous in.If the terminal conditionξhas bounded Malliavin derivative,we prove some uniqueness results for the BSDE with quadratic and linear growth in,respectively.
文摘In this paper, we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type c D δ 0＋ u（t） = f （t, u（t）, c D σ 0＋ u（t））, t ∈ [0, T ], u（0） = αu（η）, u（T ） = βu（η）, where 1 〈 δ 〈 2, 0 〈 σ 〈 1, α, β∈ R, η∈ （0, T ）, αη（1 -β） ＋ （1-α）（T βη） = 0 and c D δ 0＋ , c D σ 0＋ are the Caputo fractional derivatives. We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results. Examples are also included to show the applicability of our results.
文摘We prove an existence and uniqueness result for the Dirichlet problem for a class of elliptic equations with singular data in weighted Sobolev spaces.
