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Concentration of ground state solutions for fractional Hamiltonian systems [PDF]

Topological Methods in Nonlinear Analysis, 2017
In this paper we are concerned with the existence of ground states solutions for the following fractional Hamiltonian systems $$ \left\{ \begin{array}{ll} -_tD^α_\infty(_{-\infty}D^α_t u(t)) - λL(t)u(t)+\nabla W(t,u(t))=0,\\[0.1cm] u \in H^α(\mathbb{R},\mathbb{R}^n), \end{array} \right.\qquad(\hbox{FHS})_λ$$ where $α\in (1/2,1)$, $t\in \mathbb{R}$, $u ...
Torres, César, Zhang, Ziheng
openaire   +3 more sources

Ground state and non-ground state solutions of some strongly coupled elliptic systems [PDF]

Transactions of the American Mathematical Society, 2011
We study an elliptic system of the form L u = |
Bonheure, Denis, Moreira dos Santos, Ederson, Ramos, Miguel   +2 more
openaire   +2 more sources

Ground state for Choquard equation with doubly critical growth nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper we consider nonlinear Choquard equation \begin{equation*} -\Delta u+V(x)u=(I_\alpha*F(u))f(u)\quad {\rm in}\ \mathbb{R}^{N}, \end{equation*} where $V\in C(\mathbb{R}^N)$, $I_\alpha$ denotes the Riesz potential, $f(t)=|t|^{p-2}t+|t|^{q-2}t ...
Fuyi Li, Lei Long, Yongyan Huang, Zhanping Liang   +3 more
doaj   +1 more source

GROUND STATE SOLUTION FOR A CLASS FRACTIONAL HAMILTONIAN SYSTEMS

Journal of Applied Analysis & Computation, 2018
Summary: In this paper, we consider a class of Hamiltonian systems of the form \(_tD_\infty^\alpha(_{-\infty} D_t^\alpha u(t))+L(t) u(t)-\nabla W(t,u(t))=0\) where \(\alpha\in(\frac{1}{2},1)\), \(_{-\infty}D_t^\alpha\) and \(_tD_\infty^\alpha\) are left and right Liouville-Weyl fractional derivatives of order \(\alpha\) on the whole axis \(R ...
Lv, Ying, Tang, Chunlei, Guo, Boling
openaire   +2 more sources

Ground state solutions of inhomogeneous Bethe equations [PDF]

SciPost Physics, 2018
The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin- \frac{1}{2} 1
Belliard, Samuel, Faribault, Alexandre
openaire   +3 more sources

Rational Use of Herbal Products in Pediatric Patients Treated With Anticancer Drugs in the European Union

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Introduction The use of herbal medical preparation (HMP) is rising among pediatric oncology patients, often to manage treatment‐related symptoms. Their effectiveness remains uncertain, and the risk of herb–drug interactions is underestimated.
Orianne Mahot, Mathieu Corvaisier, Laurence Spiesser‐Robelet, Mylène Duplan, Isabelle Pellier, Delphine Bourneau‐Martin, Séverine Derbré   +6 more
wiley   +1 more source

Guidelines for Pediatric Radiotherapy Simulation: A Report From the Children's Oncology Group Radiation Oncology Discipline

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Pediatric radiation therapy presents unique challenges compared to adult treatments, including those of immobilization, potential need for sedation, and the critical importance of accurate, reproducible positioning. Additionally, heightened attention to imaging doses is necessary to minimize long‐term toxicity in survivors.
Parham Alaei, Stephen Mihalcik, Sujith Baliga, Young Kwok, Dana Casey, Eric Ehler, Christiane Burton, John C. Breneman, Daphne A. Haas‐Kogan, Suzanne L. Wolden, Arnold C. Paulino, Nadia N. Laack, Natia Esiashvili, Sarah Milgrom, Christine Hill‐Kayser, Thomas J. Fitzgerald, John A. Kalapurakal, Chia‐Ho Hua   +17 more
wiley   +1 more source

Ground State Solution of Pohožaev Type for Quasilinear Schrödinger Equation Involving Critical Exponent in Orlicz Space

Mathematics, 2019
We study the following quasilinear Schrödinger equation involving critical exponent − Δ u + V ( x ) u − Δ ( u 2 ) u = A ( x ) | u | p − 1 u + λ B ( x ) u 3 N + 2 N − 2 , u ( x
Jianqing Chen, Qian Zhang
doaj   +1 more source

Health Literacy, Self‐Efficacy and Knowledge of Sickle Cell Disease Among Caregivers

Pediatric Blood &Cancer, EarlyView.
ABSTRACT Background Sickle cell disease (SCD) is a hereditary blood disorder in which abnormal haemoglobin leads to severe anaemia, painful crises and organ failure. Caregivers’ health literacy (HL) – their ability to assess, understand and apply information, and interact with healthcare professionals – is crucial for managing children with SCD, yet ...
Melanie Bruinooge, Maite E. Houwing, Rowena L. Grohssteiner, Ferdows Atiq, Sonja A. M. C. Teuben, Mirjam P. Fransen, Marjon H. Cnossen   +6 more
wiley   +1 more source

Homoclinic solutions for second-order Hamiltonian systems with periodic potential

Boundary Value Problems, 2018
In this paper, we study the second-order Hamiltonian systems u¨−L(t)u+∇W(t,u)=0,t∈R, $$ \ddot{u}-L(t)u+\nabla W(t,u)=0,\quad t\in \mathbb{R}, $$ where L∈C(R,RN×N) $L\in C(\mathbb{R},\mathbb{R}^{N\times N})$ is a T-periodic and positive definite matrix ...
Yiwei Ye
doaj   +1 more source