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Duarte, Ronaldo C.; Souto, Marco A. S.

Nonlocal Schrödinger equations for integro-differential operators with measurable kernels. (English) Zbl 1433.35092

Topol. Methods Nonlinear Anal. 54, No. 1, 383-406 (2019).
Summary: In this paper we investigate the existence of positive solutions for the problem \[-\mathcal{L}_Ku+V(x)u=f(u) \] in \(\mathbb R^N\), where \(-\mathcal{L}_K\) is an integro-differential operator with measurable kernel \(K\). Under apropriate hypotheses, we prove by variational methods that this equation has a nonnegative solution.

Cited in 5 Documents

MSC:

35J60 Nonlinear elliptic equations
35J10 Schrödinger operator, Schrödinger equation

Keywords:

integro-differential operator; nonlocal Schrödinger equation; asymptotic potential
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Full Text: DOI Euclid

References:

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