Abstract.
In this paper we study the Schrödinger equation of the form
where λ > 0 is a parameter, a and b are positive potentials, while the nonlinear term \(f : {\mathbb{R}} \rightarrow {\mathbb{R}}\) is sublinear at infinity. Two cases will be considered: (i) f is superlinear at the origin; (ii) f does not satisfy any asymptotical property at the origin. In both situations, the existence of certain multiple weak solutions of (Pλ) are established for some λ > 0.
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This work was supported by the Istituto Nazionale di Alta Matematica, when the author visited the Department of Mathematics of the University of Catania, Italy, in June-July, 2005.
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Kristály, A. Multiple solutions of a sublinear Schrödinger equation. Nonlinear differ. equ. appl. 14, 291–301 (2007). https://doi.org/10.1007/s00030-007-5032-1
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DOI: https://doi.org/10.1007/s00030-007-5032-1