Multiple solutions of a Schrödinger type semilinear equation
Xiaochun Liu, Jianfu Yang (2000)
Commentationes Mathematicae Universitatis Carolinae
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Two nontrivial solutions are obtained for nonhomogeneous semilinear Schrödinger equations.
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Multiple solutions of a Schrödinger type semilinear equation
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A positive solution for an asymptotically linear elliptic problem on autonomous at infinity
Louis Jeanjean, Kazunaga Tanaka (2002)
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In this paper we establish the existence of a positive solution for an asymptotically linear elliptic problem on . The main difficulties to overcome are the lack of a priori bounds for Palais–Smale sequences and a lack of compactness as the domain is unbounded. For the first one we make use of techniques introduced by Lions in his work on concentration compactness. For the second we show how the fact that the “Problem at infinity” is autonomous, in contrast to just periodic, can be...
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