Simplest properties of solutions of nonlinear nonlocal equations

1994 ◽  
pp. 11-27 ◽  
Keyword(s):  
Nonlocal Equations

scholarly journals On the nonlocal equations and nonlocal charges associated with the Harry Dym hierarchy

2002 ◽  
Vol 43 (12) ◽  
pp. 6116-6128 ◽  
Author(s):  
J. C. Brunelli ◽  
G. A. T. F. da Costa
Keyword(s):  
Nonlocal Equations

scholarly journals Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

2018 ◽  
Vol 29 (2) ◽  
pp. 1428-1455 ◽  
Author(s):  
Serena Dipierro ◽  
Ovidiu Savin ◽  
Enrico Valdinoci
Keyword(s):  
Local Approximation ◽  
Nonlocal Equations

scholarly journals The Brezis–Nirenberg problem for nonlocal systems

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Luiz F. O. Faria ◽  
Olimpio H. Miyagaki ◽  
Fabio R. Pereira ◽  
Marco Squassina ◽  
Chengxiang Zhang
Keyword(s):  
Variational Methods ◽  
Weak Solutions ◽  
Fractional Laplacian ◽  
Critical Growth ◽  
Laplacian Operator ◽  
Nonlocal Equations ◽  
Suitable Sense ◽  
Regularity Of Weak Solutions ◽  
Fractional Laplacian Operator ◽  
Nirenberg Problem

AbstractBy means of variational methods we investigate existence, nonexistence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical growth and interacting, in a suitable sense, with the spectrum of the operator.

scholarly journals The Evans function for nonlocal equations

2004 ◽  
Vol 53 (4) ◽  
pp. 1095-1126 ◽  
Author(s):  
Todd Kapitula ◽  
Nathan Kutz ◽  
Bjorn Sandstede
Keyword(s):  
Evans Function ◽  
Nonlocal Equations

scholarly journals Decay estimates for solutions of nonlocal semilinear equations

2015 ◽  
Vol 218 ◽  
pp. 175-198 ◽  
Author(s):  
Marco Cappiello ◽  
Todor Gramchev ◽  
Luigi Rodino
Keyword(s):  
Water Waves ◽  
Fourier Multiplier ◽  
Sobolev Type ◽  
Decay Estimates ◽  
Shallow Water Waves ◽  
Algebraic Decay ◽  
Semilinear Equations ◽  
Nonlocal Equations ◽  
Image Position ◽  
Strong Contrast

AbstractWe investigate the decay for |x|→∞ of weak Sobolev-type solutions of semilinear nonlocal equations Pu = F(u). We consider the case when P = p(D) is an elliptic Fourier multiplier with polyhomogeneous symbol p(ξ), and we derive algebraic decay estimates in terms of weighted Sobolev norms. Our basic example is the celebrated Benjamin–Ono equation for internal solitary waves of deep stratified fluids. Their profile presents algebraic decay, in strong contrast with the exponential decay for KdV shallow water waves.

On a General Class of Nonlocal Equations

2012 ◽  
Vol 14 (4) ◽  
pp. 947-966 ◽  
Author(s):  
Przemysław Górka ◽  
Humberto Prado ◽  
Enrique G. Reyes
Keyword(s):  
General Class ◽  
Nonlocal Equations
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