Results 31 to 40 of about 8,805 (153)
Journal of Inequalities and Applications, 2020 In this paper, we consider the following sublinear fractional Schrödinger equation: ( − Δ ) s u + V ( x ) u = K ( x ) | u | p − 1 u , x ∈ R N , $$ (-\Delta)^{s}u + V(x)u= K(x) \vert u \vert ^{p-1}u,\quad x\in \mathbb{R}^{N}, $$ where s , p ∈ ( 0 , 1 ) $s,
Wen Guan, Da-Bin Wang, Xinan Hao
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, 2017 We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation \[ -{\Delta}u+ u=\big(I_\alpha*|u|^{\frac{\alpha}{N}+1}\big)|u|^{\frac{\alpha}{N}-1}u+f(x,u)\qquad \text{ in ...
Van Schaftingen, Jean, Xia, Jiankang
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Detecting Thunderstorm‐Related High‐Energy Phenomena in Weak Signals
Journal of Geophysical Research: Atmospheres, Volume 131, Issue 8, 28 April 2026.Abstract Gamma‐ray glows (GRGs) are high‐energy events associated with thunderstorms, characterized by an enhancement of the high‐energy background radiation lasting from a few seconds to several minutes. They are typically detected near their sources by balloons, aircraft, mountain‐based observatories, or at sea level in regions where thunderstorms ...
Y. Hazem +3 more
wiley +1 more source
Periodic solutions for second-order Hamiltonian systems with the p-Laplacian
Electronic Journal of Differential Equations, 2006 In this paper, we investigate the periodic solutions of Hamiltonian system with the p-Laplacian. By using Mountain Pass Theorem the existence of at least one periodic solution is obtained, Furthermore, under suitable assumptions, we obtain the ...
Weigao Ge, Yu Tian
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Advances in Difference Equations, 2019 In this paper, we study the following nonlinear Klein–Gordon–Maxwell system: {−Δu+V(x)u−(2ω+ϕ)ϕu=f(x,u)+λh(x)|u|q−2u,x∈R3,Δϕ=(ω+ϕ)u2,x∈R3,(Pλ) $$ \textstyle\begin{cases} -\Delta u+ V(x)u-(2\omega +\phi )\phi u = f(x,u)+\lambda h(x) \vert u \vert ^{q-2}u,
Chongqing Wei, Anran Li
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, 2017 Many existence and nonexistence results are known for nonnegative radial solutions $u\in D^{1,2}(\mathbb{R}^{N})\cap L^{2}(\mathbb{R}^{N},\left|x\right| ^{-\alpha }dx)$ to the equation \[ -\triangle u+\dfrac{A}{\left| x\right| ^{\alpha }}u=f\left( u ...
Rolando, Sergio
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(N,q)$(N,q)$‐Laplacian equations with one‐sided critical exponential growth
Mathematische Nachrichten, Volume 299, Issue 3, Page 675-698, March 2026.Abstract We prove the existence of two non‐trivial weak solutions for a class of quasilinear, non‐homogeneous elliptic problems driven by the (N,q)$(N,q)$‐Laplacian with one‐sided critical exponential growth in a bounded domain Ω⊂RN$\Omega \subset \mathbb {R}^{N}$. The first solution is obtained as a local minimizer of the associated energy functional;
Elisandra Gloss +2 more
wiley +1 more source
Existence of groundstates for a class of nonlinear Choquard equations in the plane
, 2017 We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation $$ -\Delta u+u=(I_\alpha*F(u))F'(u)\qquad\text{in }\mathbb{R}^2, $$ where $I_\alpha$ is the Riesz potential of order $\alpha$ on the plane $\mathbb{R}
Battaglia, Luca, Van Schaftingen, Jean
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Methodological Frameworks for Computational Electrocatalysis: From Theory to Practice
Small Methods, Volume 10, Issue 5, 9 March 2026.Computational modeling is widely used to investigate electrocatalytic reactions, yet accurately describing electrochemical interfaces remains challenging. This review outlines theoretical and computational strategies, based on density functional theory, to model reaction thermodynamics, solvation effects, applied bias, and kinetics.
Michele Re Fiorentin +8 more
wiley +1 more source
Existence and multiplicity results for some Lane–Emden elliptic systems: Subquadratic case
Advances in Nonlinear Analysis, 2015 We study the nonlinear elliptic system of Lane–Emden type -Δu = sgn(v) |v|p-1 in Ω, -Δv = f(x,u) in Ω, u = v = 0 on ∂Ω, where Ω is an open bounded subset of ℝN, N ≥ 2, p > 1 and f : Ω × ℝ → ℝ is a Carathéodory function satisfying suitable growth ...
Barile Sara, Salvatore Addolorata
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