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Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory. (English) Zbl 0964.35047
The paper deals with the existence of positive multipeak solutions of the semilinear Neumann problem $-\varepsilon^2 \Delta u+u= u^p\quad \text{in}\;\Omega,\qquad \partial u/\partial\nu=0\quad \text{on}\;\partial\Omega,$ where $$\Omega\subset\mathbb R^N$$ is a bounded and smooth domain, $$N\geq 2,$$ $$\varepsilon >0,$$ $$1<p<(N+2)/(N-2)$$ if $$N\geq 3$$ and $$p>1$$ if $$N=2,$$ and $$\nu$$ is the unit outward normal to $$\partial\Omega.$$

##### MSC:
 35J65 Nonlinear boundary value problems for linear elliptic equations 35B38 Critical points of functionals in context of PDEs (e.g., energy functionals) 35J61 Semilinear elliptic equations
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