Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials
Keyword(s):
In this study, we consider the following sublinear Schrödinger equations −Δu+Vxu=fx,u,for x∈ℝN,ux⟶0,asu⟶∞, where fx,u satisfies some sublinear growth conditions with respect to u and is not required to be integrable with respect to x. Moreover, V is assumed to be coercive to guarantee the compactness of the embedding from working space to LpℝN for all p∈1,2∗. We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions when fx,u is odd in u by using the variant fountain theorem.
Existence and multiplicity of solutions for a class of generalized quasilinear Schrödinger equations
2017 ◽
Vol 452
(1)
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pp. 578-594
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2013 ◽
Vol 403
(2)
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pp. 680-694
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2015 ◽
Vol 56
(9)
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pp. 091502
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