Existence of bounded variation solutions for a 1-Laplacian problem with vanishing potentials
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Abstract
In this work it is studied a quasilinear elliptic problem in the whole space RN involving the 1-Laplacian operator, with potentials which can vanish at infinity. The Euler–Lagrange functional is defined in a space whose definition resembles BV(RN). It is proved the existence of a nonnegative nontrivial bounded variation solution and the proof relies on a version of the Mountain Pass Theorem without the Palais–Smale condition to Lipschitz continuous functionals.
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1-Laplacian, Bounded variation functions, Mountain pass theorem
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English
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Journal of Mathematical Analysis and Applications, v. 459, n. 2, p. 861-878, 2018.
