Results 41 to 50 of about 348 (123)
Journal of Function Spaces, 2017 We study a singular Schrödinger-Kirchhoff-Poisson system by the variational methods and the Nehari manifold and we prove the existence, uniqueness, and multiplicity of positive solutions of the problem under different conditions.
Mengjun Mu, Huiqin Lu
doaj +1 more source
Non-Nehari manifold method for a class of generalized quasilinear Schrödinger equations
Applied Mathematics Letters, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jianhua Chen 0005 +2 more
openaire +2 more sources
Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\begin{equation*} {\begin{cases} -\Delta _p u+\mathcal {V}(\varepsilon x)|u|^{p-2}u+\kappa \phi u=\lambda |u|^{p-2 ...
Sihua Liang +3 more
wiley +1 more source
Journal of Function Spaces, 2020 In this paper, the nonlinear quasilinear elliptic problem with the logarithmic nonlinearity −div∇up−2∇u=axφpulogu+hxψpu in Ω⊂Rn was studied. By means of a double perturbation argument and Nehari manifold, the authors obtain the existence results.
Zhoujin Cui +4 more
doaj +1 more source
Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
The Nehari manifold for a boundary value problem involving Riemann–Liouville fractional derivative [PDF]
Advances in Difference Equations, 2018 Nuestro objetivo es investigar los siguientes problemas de valores límite no lineales de ecuaciones diferenciales fraccionarias: $$\begin{aligned} (\mathrm{P}_{\lambda})\ left\ {\ textstyle\begin {array} {l} -_{t} D_{1} ^{\alpha} ( \vert {}_{0} D_{t} ^{\alpha}(u(t)) \vert ^{p-2} {}_{0} D_{t} ^{\alpha}u(t) )\ \\\quad=f(t,u (t)) +\lambda g (t) \vert u(t)\
Kamel Saoudi +4 more
openaire +3 more sources
Planar Choquard equations with critical exponential reaction and Neumann boundary condition
Mathematische Nachrichten, Volume 297, Issue 10, Page 3847-3869, October 2024.Abstract We study the existence of positive weak solutions for the following problem: −Δu+α(x)u=∫ΩF(y,u)|x−y|μ1dyf(x,u)inΩ,∂u∂η+βu=∫∂ΩG(y,u)|x−y|μ2dνg(x,u)on∂Ω,$$\begin{equation*} \begin{aligned} \hspace*{65pt}-\Delta u + \alpha (x) u &= {\left(\int \limits _{\Omega }\frac{F(y,u)}{|x-y|^{{\mu _1}}}\;dy\right)}f(x,u) \;\;\text{in} \; \Omega,\\ \hspace ...
Sushmita Rawat +2 more
wiley +1 more source
Non‐autonomous double phase eigenvalue problems with indefinite weight and lack of compactness
Bulletin of the London Mathematical Society, Volume 56, Issue 2, Page 734-755, February 2024.Abstract In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, −Δpau−Δqu=λm(x)|u|q−2uinRN,$$\begin{equation*} \hspace*{3pc}-\Delta _p^a u-\Delta _q u =\lambda m(x)|u|^{q-2}u \quad \mbox{in} \,\, \mathbb {R}^N, \end{equation*}$$where N⩾2$N \geqslant 2$, 1
Tianxiang Gou, Vicenţiu D. Rădulescu
wiley +1 more source
Ground states for Schrodinger-Poisson systems with three growth terms
Electronic Journal of Differential Equations, 2014 In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V ...
Hui Zhang, Fubao Zhang, Junxiang Xu
doaj
Journal of Function Spaces, Volume 2024, Issue 1, 2024.In this paper, we consider the weighted m‐biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao’s inequality. Finally, we proved the blow‐up of solutions in finite time.
Ayşe Fidan +3 more
wiley +1 more source