Abstract
In this paper, we consider the following nonhomogenous Schrödinger–Kirchhoff type problem
where constants a > 0, b ≥ 0, N = 1, 2 or 3, \({V\in C(R^{N},R)}\), \({f\in C(R^{N} \times R, R)}\) and \({g\in L^{2}(R^{N})}\). Under more relaxed assumptions on the nonlinear term f that are much weaker than those in Chen and Li (Nonlinear Anal RWA 14:1477–1486, 2013), using some new proof techniques especially the verification of the boundedness of Palais–Smale sequence, a new result on multiplicity of nontrivial solutions for the problem (1.1) is obtained, which sharply improves the known result of Theorem 1.1 in Chen and Li (Nonlinear Anal RWA 14:1477–1486, 2013).
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This work is partly supported by the National Natural Science Foundation of China (11361048), the Foundation of Education of Commission of Yunnan Province (2014Z153, 2013Y015) and the Youth Program of Yunnan Provincial Science and Technology Department (2013FD046).
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Cheng, B. A New Result on Multiplicity of Nontrivial Solutions for the Nonhomogenous Schrödinger–Kirchhoff Type Problem in R N . Mediterr. J. Math. 13, 1099–1116 (2016). https://doi.org/10.1007/s00009-015-0527-1
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DOI: https://doi.org/10.1007/s00009-015-0527-1