Abstract

Using J we can easily see some qualitative properties of the solutions, for example we can determine the values where u changes sign, has a local maxima or minima, or changes concavity. We also use this functional to construct, for any k is an element of N, nonlinearities f such that this problem has at least two bound state solutions that change sign j times, for j = 0, 1, ... , k - 1. And another f such that this problem has a unique ground state solution, and at least two bound state solutions that change sign one time. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.