Results 41 to 50 of about 2,421 (92)
Identification of discontinuous parameters in double phase obstacle problems
Advances in Nonlinear Analysis, 2022 In this article, we investigate the inverse problem of identification of a discontinuous parameter and a discontinuous boundary datum to an elliptic inclusion problem involving a double phase differential operator, a multivalued convection term (a ...
Zeng Shengda +3 more
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Standing wave solution for the generalized Jackiw-Pi model
Advances in Nonlinear Analysis, 2022 We study the existence and nonexistence of the standing wave solution for the generalized Jackiw-Pi model by using variational method. Depending on interaction strength λ\lambda , we have three different situations.
Huh Hyungjin +3 more
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On the critical Choquard-Kirchhoff problem on the Heisenberg group
Advances in Nonlinear Analysis, 2022 In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
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A strongly indefinite Choquard equation with critical exponent due to the Hardy-Littlewood-Sobolev inequality [PDF]
arXiv, 2017 In this paper we are concerned with the following nonlinear Choquard equation $$-\Delta u+V(x)u =\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^{\mu}}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N, $$ where $N\geq4$, $0<\mu
arxiv
Weighted critical exponents of Sobolev-type embeddings for radial functions
Advanced Nonlinear Studies, 2022 In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.
Su Jiabao, Wang Cong
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Schrodinger equation with critical Sobolev exponent [PDF]
arXiv, 2004 In this paper we study the existence of solutions and their concentration phenomena of a singularly perturbed semilinear Schrodinger equation with the presence of the critical Sobolev exponent.
arxiv
Multiple solutions to multi-critical Schrödinger equations
Advanced Nonlinear Studies, 2022 In this article, we investigate the existence of multiple positive solutions to the following multi-critical Schrödinger equation: (0.1)−Δu+λV(x)u=μ∣u∣p−2u+∑i=1k(∣x∣−(N−αi)∗∣u∣2i∗)∣u∣2i∗−2uinRN,u∈H1(RN),\left\{\begin{array}{l}-\Delta u+\lambda V\left(x)u=
Xu Ziyi, Yang Jianfu
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A note on the Neumann problem [PDF]
arXiv, 2009 In this paper we provide an application to the Neumann problem of a recent three critical points theorem.
arxiv
Critical nonlocal Schrödinger-Poisson system on the Heisenberg group
Advances in Nonlinear Analysis, 2021 In this paper, we are concerned with the following a new critical nonlocal Schrödinger-Poisson system on the Heisenberg group:
Liu Zeyi +4 more
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On the Dirichlet Problem Generated by the Maz'ya--Sobolev Inequality [PDF]
arXiv, 2011 We discuss the attainability of sharp constants for the Maz'ya--Sobolev inequalities in wedges, "perturbed" wedges and bounded domains.
arxiv