We consider periodic solutions of the following problem associated with the fractional Laplacian $$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$(-∂xx)su(x)+F′(u(x))=0,u(x)=u(x+T),inR,where $$(-\partial _{xx})^s$$(-∂xx)s denotes the… Click to show full abstract
We consider periodic solutions of the following problem associated with the fractional Laplacian $$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$(-∂xx)su(x)+F′(u(x))=0,u(x)=u(x+T),inR,where $$(-\partial _{xx})^s$$(-∂xx)s denotes the usual fractional Laplace operator with $$0
               
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