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 \(\partial\Omega.\)


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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