The main purpose of this paper is to establish the existence of a solution of the semilinear Schrodinger equation -Delta u + V(x)u= f(u). om R-2 where V is a 1-periodic function with respect to x, 0 lies in a gap of the spectrum of -Delta + V, and f(s) behaves like +/- exp(alpha s(2)) when s -&rt; +/-infinity.
On a Schrodinger equation with periodic potential and critical growth in R-2 / J.M. do O, B. Ruf. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 13:2(2006), pp. 167-192.
On a Schrodinger equation with periodic potential and critical growth in R-2
B. RufUltimo
2006
Abstract
The main purpose of this paper is to establish the existence of a solution of the semilinear Schrodinger equation -Delta u + V(x)u= f(u). om R-2 where V is a 1-periodic function with respect to x, 0 lies in a gap of the spectrum of -Delta + V, and f(s) behaves like +/- exp(alpha s(2)) when s -&rt; +/-infinity.
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