Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane
Copyright policy )Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane
Abstract We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equations - Δ u + u = ( I α * F ( u ) ) F ′ ( u ) in ℝ 2 , -\Delta u+u=\bigl{(}I_{\alpha}*F(u)\bigr{)}F^{\prime}(u)\quad\text{in }\mathbb% {R}^{2}, where I α {I_{\alpha}} is the Riesz potential of order α on the plane ℝ 2 {\mathbb{R}^{2}} under general nontriviality, growth and subcriticality on the nonlinearity F ∈ C 1 ( ℝ , ℝ ) {F\in C^{1}(\mathbb{R},\mathbb{R})} .
- Université Catholique de Louvain Belgium
- Roma Tre University Italy
- Sapienza University of Rome Italy
35j91, Variational methods for second-order elliptic equations, choquard equation, semilinear elliptic problem, variational methods, Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian, 35j20, Mathematical analysis, Partial differential equations, variational method, 35J91, 35J20, Choquard Equation; Semilinear Elliptic Problem; Variational Method; Statistical and Nonlinear Physics; Mathematics (all), ground state solutions, Mathematics - Analysis of PDEs, QA1-939, nonlinear Choquard equations, FOS: Mathematics, Mathematics, Analysis of PDEs (math.AP)
35j91, Variational methods for second-order elliptic equations, choquard equation, semilinear elliptic problem, variational methods, Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian, 35j20, Mathematical analysis, Partial differential equations, variational method, 35J91, 35J20, Choquard Equation; Semilinear Elliptic Problem; Variational Method; Statistical and Nonlinear Physics; Mathematics (all), ground state solutions, Mathematics - Analysis of PDEs, QA1-939, nonlinear Choquard equations, FOS: Mathematics, Mathematics, Analysis of PDEs (math.AP)
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