We consider a class of modified Schrödinger-Poisson systems with general nonlinearity by variational methods. The existence and multiplicity of solutions are obtained. Besides, when $ V(x) = 1 $ and $ f(x, u) = |u|^{p-2}u $, we obtain some existence and non-existence results for the modified Schrödinger-Poisson systems.
Citation: Xian Zhang, Chen Huang. Existence, multiplicity and non-existence of solutions for modified Schrödinger-Poisson systems[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3482-3503. doi: 10.3934/mbe.2023163
We consider a class of modified Schrödinger-Poisson systems with general nonlinearity by variational methods. The existence and multiplicity of solutions are obtained. Besides, when $ V(x) = 1 $ and $ f(x, u) = |u|^{p-2}u $, we obtain some existence and non-existence results for the modified Schrödinger-Poisson systems.
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