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Normalized solutions for the double-phase problem with nonlocal reaction
Advances in Nonlinear AnalysisIn this article, we consider the double-phase problem with nonlocal reaction. For the autonomous case, we introduce the methods of the Pohozaev manifold, Hardy-Littlewood Sobolev subcritical approximation, adding the mass term to prove the existence and ...
Cai Li, Zhang Fubao
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Normalized concentrating solutions to nonlinear elliptic problems [PDF]
, 2021 We prove the existence of solutions (λ,v)∈R×H1(Ω) of the elliptic problem {−Δv+(V(x)+λ)v=vp in Ω,v>0,∫Ωv2dx=ρ. Any v solving such problem (for some λ) is called a normalized solution, where the normalization is settled in L2(Ω).
Pellacci B. +3 more
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Existence of solutions to a normalized F-infinity Laplacian equation
Electronic Journal of Differential Equations, 2014 In this article, for a continuous function F that is twice differentiable at a point $x_0$, we define the normalized F-infinity Laplacian $\Delta_{F; \infty}^N$ which is a generalization of the usual normalized infinity Laplacian. Then for a bounded
Hua Wang, Yijun He
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Positive Normalized Solutions to a Kind of Fractional Kirchhoff Equation with Critical Growth
Fractal and FractionalIn this paper, we have investigated the existence of normalized solutions for a class of fractional Kirchhoff equations involving nonlinearity and critical nonlinearity. The nonlinearity satisfies L2-supercritical conditions.
Shiyong Zhang, Qiongfen Zhang
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Normalized solutions for the discrete Schrödinger equations
Boundary Value Problems, 2023 In the present paper, we consider the existence of solutions with a prescribed l 2 $l^{2}$ -norm for the following discrete Schrödinger equations, { − Δ 2 u k − 1 − f ( u k ) = λ u k k ∈ Z , ∑ k ∈ Z | u k | 2 = α 2 , $$ \textstyle\begin{cases} -\Delta ...
Qilin Xie, Huafeng Xiao
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On Iterative Solution of the Extended Normal Equations [PDF]
SIAM Journal on Matrix Analysis and Applications, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Henri Calandra +3 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2023 In this paper, we look for solutions to the following critical Schrödinger system $$\begin{cases} -\Delta u+(V_1+\lambda_1)u=|u|^{2^*-2}u+|u|^{p_1-2}u+\beta r_1|u|^{r_1-2}u|v|^{r_2}&{\rm in}\ \mathbb{R}^N,\\ -\Delta v+(V_2+\lambda_2)v=|v|^{2^*-2}v+|v ...
Lei Long, Xiaojing Feng
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Normalized solutions for a class of scalar field equations involving mixed fractional Laplacians
Advanced Nonlinear Studies, 2022 The purpose of this article is to establish sharp conditions for the existence of normalized solutions to a class of scalar field equations involving mixed fractional Laplacians with different orders.
Luo Tingjian, Hajaiej Hichem
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NORMAL BGG SOLUTIONS AND POLYNOMIALS [PDF]
International Journal of Mathematics, 2012 First BGG operators are a large class of overdetermined linear differential operators intrinsically associated to a parabolic geometry on a manifold. The corresponding equations include those controlling infinitesimal automorphisms, higher symmetries and many other widely studied PDE of geometric origin.
Cap, Andreas +2 more
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