Results 21 to 30 of about 377 (53)
Nonzero positive solutions of a multi-parameter elliptic system with functional BCs
, 2017 We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and covers the case of
Infante, Gennaro
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Groundstates of the Choquard equations with a sign-changing self-interaction potential
, 2018 We consider a nonlinear Choquard equation $$ -\Delta u+u= (V * |u|^p )|u|^{p-2}u \qquad \text{in }\mathbb{R}^N, $$ when the self-interaction potential $V$ is unbounded from below.
Battaglia, Luca, Van Schaftingen, Jean
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Regularity of minimizers for double phase functionals of borderline case with variable exponents
Advances in Nonlinear AnalysisThe aim of this article is to study regularity properties of a local minimizer of a double phase functional of type ℱ(u)≔∫Ω(∣Du∣p(x)+a(x)∣Du∣p(x)log(e+∣Du∣))dx,{\mathcal{ {\mathcal F} }}\left(u):= \mathop{\int }\limits_{\Omega }({| Du| }^{p\left(x)}+a ...
Ragusa Maria Alessandra +1 more
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Duality methods for a class of quasilinear systems
, 2013 Duality methods are used to generate explicit solutions to nonlinear Hodge systems, demonstrate the well-posedness of boundary value problems, and reveal, via the Hodge-B\"acklund transformation, underlying symmetries among superficially different forms ...
Agarwal +21 more
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A Note on why Enforcing Discrete Maximum Principles by a simple a Posteriori Cutoff is a Good Idea
, 2012 Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we enforce the discrete maximum principle by performing a simple cutoff.
Kreuzer, Christian
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Stability and critical dimension for Kirchhoff systems in closed manifolds
Advanced Nonlinear StudiesThe Kirchhoff equation was proposed in 1883 by Kirchhoff [Vorlesungen über Mechanik, Leipzig, Teubner, 1883] as an extension of the classical D’Alembert’s wave equation for the vibration of elastic strings. Almost one century later, Jacques Louis Lions [“
Hebey Emmanuel
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Advances in Nonlinear Analysis, 2017 The core of this paper concerns the existence (via regularity) of weak solutions in W01,2${W_{0}^{1,2}}$ of a class of elliptic systems such ...
Boccardo Lucio, Orsina Luigi
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A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient
Advanced Nonlinear Studies, 2020 We consider the elliptic equation -Δu=uq|∇u|p{-\Delta u=u^{q}|\nabla u|^{p}} in ℝn{\mathbb{R}^{n}} for any p>2{p>2} and q>0{q>0}. We prove a Liouville-type theorem, which asserts that any positive bounded solution is constant.
Filippucci Roberta +2 more
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High-energy solutions for coupled Schrödinger systems with critical growth and lack of compactness
Advances in Nonlinear AnalysisThis article deals with the existence of high-energy positive solutions for the following coupled Schrödinger system with critical exponent: −Δu+V1(x)u=μ1u3+βuv2,x∈Ω,−Δv+V2(x)v=βu2v+μ2v3,x∈Ω,u,v∈D01,2(Ω)\left\{\begin{array}{l}-\Delta u+{V}_{1}\left(x)u={\
Guan Wen, Wang Da-Bin, Xie Huafei
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Advances in Nonlinear AnalysisLet (ℳ,g)\left({\mathcal{ {\mathcal M} }},g) and (K,κ)\left({\mathcal{K}},\kappa ) be two Riemannian manifolds of dimensions NN and mm, respectively. Let ω∈C2(ℳ)\omega \in {C}^{2}\left({\mathcal{ {\mathcal M} }}) satisfy ω>0\omega \gt 0.
Chen Wenjing, Wang Zexi
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