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Bound state solutions for a class of Nonlinear Elliptic Equations with Hardy potential and Berestycki-Lions type conditions. (English) Zbl 1490.35183

Summary: By using the variational methods, a class of Nonlinear Elliptic Equations with the Hardy potential and Berestycki-Lions type conditions is studied and a bound state solution is obtained.

MSC:

35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J20 Variational methods for second-order elliptic equations
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References:

[1] Li, G.-D.; Li, Y.-Y.; Tang, C.-L., Existence and asymptotic behavior of ground state solutions for Schrödinger equations with Hardy potential and Berestycki-Lions type conditions, J. Differential Equations, 275, 77-115 (2021) · Zbl 1455.35066
[2] Berestycki, H.; Lions, P.-L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Ration. Mech. Anal., 82, 4, 313-345 (1983) · Zbl 0533.35029
[3] Chen, Z.; Zou, W., On coupled systems of Schrödinger equations, Adv. Differential Equations, 16, 7-8, 775-800 (2011) · Zbl 1232.35063
[4] Jeanjean, L., Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Anal., 28, 10, 1633-1659 (1997) · Zbl 0877.35091
[5] Jeanjean, L.; Tanaka, K., A remark on least energy solutions in \(\mathbf{R}^N\), Proc. Amer. Math. Soc., 131, 8, 2399-2408 (2003) · Zbl 1094.35049
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