scholarly journals Boundary regularity for fully nonlinear integro-differential equations

2016 ◽  
Vol 165 (11) ◽  
pp. 2079-2154 ◽  
Author(s):  
Xavier Ros-Oton ◽  
Joaquim Serra
Keyword(s):  
Differential Equations ◽  
Boundary Regularity ◽  
Fully Nonlinear

scholarly journals Comparison Theorem for Nonlinear Path-Dependent Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Falei Wang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Comparison Theorem ◽  
Parabolic Partial Differential Equation ◽  
Basic Variable ◽  
Partial Differential ◽  
Fully Nonlinear ◽  
Path Dependent

We introduce a type of fully nonlinear path-dependent (parabolic) partial differential equation (PDE) in which the pathωton an interval [0,t] becomes the basic variable in the place of classical variablest,x∈[0,T]×ℝd. Then we study the comparison theorem of fully nonlinear PPDE and give some of its applications.

scholarly journals Systems of differential equations with fully nonlinear boundary conditions

1997 ◽  
Vol 56 (2) ◽  
pp. 197-208 ◽  
Author(s):  
H.B. Thompson
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Neumann Boundary ◽  
Nonlinear Boundary Conditions ◽  
Fully Nonlinear ◽  
Systems Of Differential Equations ◽  
Special Cases

We give sufficient conditions involving f, g and ω in order that systems of differential equations of the form y″ = f(x, y, y′), x in [0, 1] with fully nonlinear boundary conditions of the form g((y(0), y(1)), (y′(0), y′(1))) = 0 have solutions y with (x, y) in . We use Schauder degree theory in a novel space. Well known existence results for the Picard, the periodic and the Neumann boundary conditions follow as special cases of our results.

Sign in / Sign up

Export Citation Format

Share Document