Results 41 to 50 of about 2,202 (138)
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: $$\begin{aligned} (\mathrm{P}_{\lambda})\ left\ {\ textstyle\begin {array} {l} -_{t} D_{1} ^{\alpha} ( \vert {}_{0} D_{t} ^{\alpha}(u(t)) \vert ^{p-2} {}_{0} D_{t} ^{\alpha}u(t) )\ \\\quad=f(t,u (t)) +\lambda g (t) \vert u(t)\
Kamel Saoudi +4 more
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Nehari manifold approach for superlinear double phase problems with variable exponents
Annali di Matematica Pura ed Applicata (1923 -), 2023 AbstractIn this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on the nonlinearity, we prove a multiplicity result for such problems whereby we show the existence of a positive solution, a negative one and a solution with changing ...
Ángel Crespo-Blanco, Patrick Winkert
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Positive solutions for asymptotically linear problems in exterior domains
, 2016 The existence of a positive solution for a class of asymptotically lin- ear problems in exterior domains is established via a linking argument on the Nehari manifold and by means of a barycenter ...
Maia, Liliane A., Pellacci, Benedetta
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Studies in Applied Mathematics, Volume 156, Issue 4, April 2026.ABSTRACT We study the nonlinear Schrödinger equation with a competing cubic–quintic power‐law nonlinearity on the waveguide domain Rx×TLy$\mathbb {R}_x \times \mathbb {T}_{L_y}$. This model is globally well‐posed and admits line solitary wave solutions, whose transverse (in‐)stability is numerically investigated.
Christian Klein, Christof Sparber
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Multiplicity results for logarithmic double phase problems via Morse theory
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 4178-4201, December 2025.Abstract In this paper, we study elliptic equations of the form −divL(u)=f(x,u)inΩ,u=0on∂Ω,$$\begin{align*} -\operatorname{div}\mathcal {L}(u)=f(x,u)\quad \text{in }\Omega, \quad u=0 \quad \text{on } \partial \Omega, \end{align*}$$where divL$\operatorname{div}\mathcal {L}$ is the logarithmic double phase operator given by div|∇u|p−2∇u+μ(x)|∇u|q(e+|∇u ...
Vicenţiu D. Rădulescu +2 more
wiley +1 more source
Fractional Q$Q$‐curvature on the sphere and optimal partitions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara +2 more
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Variational properties and orbital stability of standing waves for NLS equation on a star graph
, 2014 We study standing waves for a nonlinear Schr\"odinger equation on a star graph {$\mathcal{G}$} i.e. $N$ half-lines joined at a vertex. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\alpha\leqslant 0 ...
Adami, R. +3 more
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Nehari manifold and multiplicity result for elliptic equation involving p-laplacian problems
Boletim da Sociedade Paranaense de Matemática, 2018 This article shows the existence and multiplicity of positive solutions of the $p$-Laplacien problem $$\displaystyle -\Delta_{p} u=\frac{1}{p^{\ast}}\frac{\partial F(x,u)}{\partial u} + \lambda a(x)|u|^{q-2}u \quad \mbox{for } x\in\Omega;\quad \quad u=0,\quad \mbox{for } x\in\partial\Omega$$ where $\Omega$ is a bounded open set in $\mathbb{R}^n$ with ...
Khaled Ben Ali, Abdeljabbar Ghanmi
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Superlinear perturbations of a double‐phase eigenvalue problem
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract We consider a perturbed version of an eigenvalue problem for the double‐phase operator. The perturbation is superlinear, but need not satisfy the Ambrosetti–Robinowitz condition. Working on the Sobolev–Orlicz space W01,η(Ω)$ W^{1,\eta }_{0}(\Omega)$ with η(z,t)=α(z)tp+tq$ \eta (z,t)=\alpha (z)t^{p}+t^{q}$ for 1
Yunru Bai +2 more
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Normalized solutions of the critical Schrödinger–Bopp–Podolsky system with logarithmic nonlinearity
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we study the following critical Schrödinger–Bopp–Podolsky system driven by the p$p$‐Laplace operator and a logarithmic nonlinearity: −Δpu+V(εx)|u|p−2u+κϕu=λ|u|p−2u+ϑ|u|p−2ulog|u|p+|u|p*−2uinR3,−Δϕ+a2Δ2ϕ=4π2u2inR3.$$\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