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Nonlinear nonlocal elliptic problems in ℝ3: existence results and qualitative properties

Lü Dengfeng, Dai Shu-Wei

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230147

We consider the following nonlinear nonlocal elliptic problem: [formula], where a, b > 0 are constants, λ > 0 is a parameter, α ∈ (0,3), and G ∈ C1 (R,R). By using variational methods, we establish the existence of least energy solutions for the above equation under conditions on the nonlinearity G we believe to be almost necessary. Some qualitative properties of the least energy solutions are also obtained