Unbounded perturbations of resonant Schrödinger equations
David G. Costa, Hossein Tehrani · Contemporary mathematics - American Mathematical Society · 2004
We consider the question of existence of solution for resonant Schrodinger equations of the form i¢u + V (x)u = ‚u + g(x;u); x 2 N ; where the potential V (x) vanishes at infinity and ‚ < 0 is an eigenvalue of the corresponding Schrodinger operator LV := ¢ + V (x). The (possibly un- bounded) perturbation g(x;u) is assumed to have at most a sublinear growth and satisfy a variant of the Ahmad-Lazer-Paul condition. (P‚) i¢u + V (x)u = ‚u + g(x;u) ; x 2 › =R N ; when the parameter ‚ = b ‚ < 0 is an eigenvalue of the Schrodinger operator LV := i¢+V (x) inR N. Here, the potential V 2 C(R N ;R) is such that limjxj!1 V (x) = 0 and LV has negative eigenvalues, while the perturbation g 2 C(R N £R;R) has a