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Titlebook: Contributions to Nonlinear Elliptic Equations and Systems; A Tribute to Djairo Alexandre Nolasco de Carvalho,Bernhard Ruf,Thierry Book 201

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https://doi.org/10.1007/978-3-642-58895-2We investigate the asymptotic behavior of positive ground states for Hénon type systems involving a fractional Laplacian on a bounded domain, when the powers of the nonlinearity approach the Sobolev critical exponent.
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https://doi.org/10.1007/978-3-642-59006-1In this paper we prove that the sub-supersolution method works for general Kirchhoff systems. We apply the cited method to prove the existence of positive solutions for some specific models.
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,Nonexistence of positive classical solutions for the nonlinear Schrödinger equation with unbounded We establish a nonexistence result of positive classical solutions for a class of nonlinear Schrödinger equations involving unbounded, singular at the origin or decaying weights in dimension two. Our approach relies on the average argument.
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Positive solutions for certain classes of fourth-order ordinary elliptic systems,Using fixed-point techniques, we study the existence of positive solutions for a class of fourth-order ordinary elliptic systems. To this end, we reduce our problem to an appropriate functional differential equation.
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