Existence of normalized solutions for a Sobolev supercritical Schrodinger equation

This paper studies the existence of normalized solutions for the following Schrodinger equation with Sobolev supercritical growth: {-triangle u + V(x)u + lambda u = f (u) + mu |u|(p-2)u , in R-N, integral(RN) |u|(2)dx = a(2), where p > 2* := 2N/N- 2, N >= 3, a > 0, lambda is an element of R is an unknown Lagrange multiplier, V is an element of C (R-N, R), f satisfies weak mass subcritical conditions. By employing the truncation technique, we establish the existence of normalized solutions to this Sobolev supercritical problem. Our primary contribution lies in our initial exploration of the case p > 2*, which represents an unfixed frequency problem.