scholarly journals Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

Bernoulli ◽  
2007 ◽  
Vol 13 (2) ◽  
pp. 423-446 ◽  
Author(s):  
Brahim Boufoussi ◽  
Jan Van Casteren ◽  
N. Mrhardy
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Stochastic Differential Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Doubly Stochastic ◽  
Nonlinear Neumann Boundary Conditions

STOCHASTIC CAHN–HILLIARD PARTIAL DIFFERENTIAL EQUATIONS WITH LÉVY SPACETIME WHITE NOISES

2006 ◽  
Vol 06 (02) ◽  
pp. 229-244 ◽  
Author(s):  
LIJUN BO ◽  
YONGJIN WANG
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Local Solution ◽  
Neumann Boundary Conditions ◽  
Partial Differential ◽  
White Noises

In this paper, we consider a class of stochastic Cahn–Hilliard partial differential equations driven by Lévy spacetime white noises with Neumann boundary conditions. By a dedicate construction we prove that a (unique) local solution exists for the SPDE under some mild assumptions on the coefficients.

scholarly journals Multiple solutions for a class of bi-nonlocal problems with nonlinear Neumann boundary conditions

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Ghasem A. Afrouzi ◽  
Z. Naghizadeh ◽  
Nguyen Thanh Chung
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Weak Solutions ◽  
Multiple Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Nonlocal Problems ◽  
Mapping Theory ◽  
Nonlinear Neumann Boundary Conditions

In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using $(S_+)$ mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provied that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.

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