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Multiplicity results for a class of semilinear elliptic equations on \(\mathbb{R}^ m\). (English) Zbl 0866.35043

Existence and multiplicity results are proved for solutions of the problem \[ -\Delta u+u=f(x,u), \quad u\in H^1 (\mathbb{R}^m) \] where \(m\geq 1\) and \(f\) satisfies suitable subcritical and periodic assumptions. In the proofs the mountain pass theorem and the concentration-compactness method are used.
Reviewer: S.Tersian (Russe)

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J20 Variational methods for second-order elliptic equations
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References:

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