Sign changing solutions of some integral equaitons with critical sobolev exponents

Details Sign changing solutions of some integral equaitons with critical sobolev exponents Sign changing solutions of some integral equaitons with critical sobolev exponents

2010-04-17

arxiv.org/abs/1004.2973v1

Mathematics

Analysis of PDEs

Scientific paper

In this note we prove that: \begin{theorem} for $2\leq s<\frac{n}{2}$ or $1\leq s<\frac{2n}{n+1}$ or $1\leq s<\frac{n}{2}$ but n is even, $(-\Delta)^{s}(u)=|u|^{q-2}u,q=\frac{2n}{n-2s}$ has infinitely many sign changing solutions or equivalently we can say that there exist solutions $u_{k}$ such that $\int u_{k}(-\Delta)^{s}(u_{k})dx \to \infty$ as $k\to \infty$ \end{theorem}

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