
 
An Alternative Way of Utilizing Fixed Point Theory 
 
Citation： 
Dapeng DU.An Alternative Way of Utilizing Fixed Point Theory[J].Chinese Annals of Mathematics B,2020,41(6):861~872 
Page view： 38
Net amount： 28 
Authors： 
Dapeng DU; 


Abstract： 
The author proposes an alternative way of using fixed point theory to get the existence for semilinear equations. As an example, a nonlocal ordinary differential equation is considered. The idea is to solve homogeneous equations in the linearization. One feature of this method is that it does not need the equation to have special structures, for instance, variational structures, maximum principle, etc. Roughly speaking, the existence comes from good properties of the suitably linearized equation. The idea may have wider application. 
Keywords： 
Existence, Semilinear equations, Fixed point theory, Homogeneous linearization 
Classification： 
35A99 

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