Existence of infinitely many solutions for a class of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions in RN

AbstractIn this paper, we study the following kind of Schrödinger–Poisson equations without any growth and Ambrosetti–Rabinowitz conditions: −Δu+V(x)u+(|x|−1∗u2)u−λu=f(u),x∈RN, where λ<0, V(x)∈C[0,+∞) is a potential function and satisfies certain conditions. By using variational method, truncation function and Fountain Theorem, we get the existence of infinitely many solutions to revised equations. Then we use the Moser iteration to obtain the existence of infinitely many solutions to original Schrödinger–Poisson equations.Keywords: Schrödinger–Poisson equationtruncation functionfountain theoremAMS Subject Classifications: 35A1535B38 Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingSupported by the National Natural Science Foundation of China [grant number 11861021]; the Natural Science Research Project of Department of Education of Guizhou Province [grant number QJJ2022015, QJJ2022047]; the Natural Science Research Project of Guizhou Minzu University [grant number GZMUZK[2022]YB23].