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Solutions of a nonlinear Schrödinger equation

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  • This paper deals with existence and multiplicity of solutions to the nonlinear Schrödinger equation of the type

    $-\Delta u + (\lambda a(x) + a_0(x))u = f(x, u), u\in H^1(\mathbb R^N).$

    We improve some previous results in two respects: we do not require $a_0$ to be positive on one hand, and allow $f(x, u)$ to be critical nonlinear on the other hand.

    Mathematics Subject Classification: Primary: 35Q55; Secondary: 58E05.


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