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Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations
G-Brownian motion super linear expectation normal distribution backward stochastic differential equations
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2010/11/30
This paper first studies super linear G-expectation. Uniqueness and existence theorem for backward stochastic differential equations (BSDEs) under super linear expectation is stablished to provide pro...
Asymptotic stability of solutions to abstract differential equations
Nonlinear inequality Asymptotic stability Abstract differential equations
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2010/12/15
An evolution problem for abstract differential equations is studied. The typical problem is:
˙ u = A(t)u+F(t,u), t ≥ 0; u(0) = u0; ˙ u =du dt ∗)Here A(t) is a linear bounded operator in a Hilbe...
Solutions Near Singular Points to the Eikonal and Related First Order Non-linear Partial Differential Equations in Two Independent Variables
Singular Points Eikonal Partial Differential Equations
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2010/11/1
A detailed study of solutions to the first order partial differential equation H(x,y,z_x,z_y)=0, with special emphasis on the eikonal equation z_x^2+z_y^2=h(x,y), is made near points where the equatio...