SEMILINEAR EQUATIONS OF GRADIENT TYPE IN HILBERT SPACES AND APPLICATIONS TO DIFFERENTIAL EQUATIONS

1981 ◽  
pp. 269-282
Author(s):  
Jean Mawhin
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Semilinear Equations ◽  
Gradient Type

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

Oscillation Criteria for Semilinear Equations in General Domains

1976 ◽  
Vol 19 (2) ◽  
pp. 137-144 ◽  
Author(s):  
W. Allegretto
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Recent Work ◽  
Linear Equations ◽  
Oscillation Theory ◽  
General Nature ◽  
Nonlinear Ordinary Differential Equations ◽  
Exterior Domains ◽  
Semilinear Equations

Oscillation theory for nonlinear ordinary differential equations has been extensively developed in recent years by several authors. We refer the reader to the recent paper by Noussair and Swanson, [2], where an extensive bibliography may be found. The situation is somewhat different for the case of second order partial differential equations, an area which has recently been virtually untouched, except for the establishment of criteria which depend on a comparison with suitable linear equations and therefore are essentially linear in nature. A bibliography of such results may also be found in [2]. Of a more general nature have been the paper by the author [1], and the more recent work of Noussair and Swanson, [2]. Although the methods employed and the equations considered in [1] and [2] are different, both papers obtained results only for a class of exterior domains of Rn, of which the typical example is the complement of a bounded sphere.

Existence of Solutions of Abstract Differential Equations in a Local Space

1973 ◽  
Vol 16 (2) ◽  
pp. 239-244
Author(s):  
M. A. Malik
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Differential Equations ◽  
Complex Plane ◽  
Hilbert Spaces ◽  
Scalar Product ◽  
Existence Of Solutions ◽  
Closed Linear Operator ◽  
Abstract Differential Equations ◽  
Local Space

Let H be a Hilbert space; ( , ) and | | represent the scalar product and the norm respectively in H. Let A be a closed linear operator with domain DA dense in H and A* be its adjoint with domain DA*. DA and DA*are also Hilbert spaces under their respective graph scalar product. R(λ; A*) denotes the resolvent of A*; complex plane. We write L = D — A, L* = D — A*; D = (l/i)(d/dt).

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