How to prove the x_N-odd solution of -\Delta u+|u|^pu=f in B_1, where f is x_N-odd?

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Giorgio Metafune

I guess you assume Dirichelet bc so that the above problem is uniquely solvable in Holder spaces, since h(t)=|t|^pt is C^1 and increasing. If v(x',x_N)=-u(x',-x_N), then v solves the same problem as u, hence u=v.

Chen Huyuan

Thanks, I got it.

Бойков Владимир

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