Existence and bifurcation of periodic solutions to the Lp-Minkowski problem with indefinite weight

This paper is devoted to the existence and bifurcation of positive periodic solutions for Lp-Minkowski problem with indefinite weight. We provide new sufficient conditions for the existence of at least one positive periodic solution. The main tools are Leray-Schauder alternative principle and a global continuation theorem by Manasevich-Mawhin. Using the numerical bifurcation theory, we study the dynamic behaviors of periodic solutions in the cases of indefinite and positive weight, where the weight term is a simple sinusoidal function. In the positive weight case, the multiplicity of positive periodic solutions is detected for the first time in the LpMinkowski problem, which is generated by a saddle-node bifurcation. (c) 2024 Elsevier Inc. All rights reserved.