Solitary waves for coupled nonlinear elliptic system with nonhomogeneous nonlinearities
The aim of this paper is to prove the existence, nonexistence and multiplicity of nontrivial solutions of some coupled nonlinear elliptic systems with nonhomogeneous nonlinearities by applying Morse theory, direct analysis methods and the Krasnosel'skii-Rabinowitz global bifurcation theorem. Further, the asymptotical behavior of positive solutions is studied, and some properties of such solutions are established. Moreover, comparing to previous works on the homogenous case, the author combines the Mountain-Pass theorem in convex sets and the Nehari constraint method to prove the existence and multiplicity of nontrivial solutions in the nonhomogeneous case.
coupled nonlinear elliptic systems, nonhomogeneous nonlinearities
scientific article; zbMATH DE number 6715637
scientific article