Results 21 to 30 of about 216,697 (310)
Infinitely many solutions of degenerate quasilinear Schrödinger equation with general potentials
Boundary Value Problems, 2021 In this paper, we study the following quasilinear Schrödinger equation: − div ( a ( x , ∇ u ) ) + V ( x ) | x | − α p ∗ | u | p − 2 u = K ( x ) | x | − α p ∗ f ( x , u ) in R N , $$ -\operatorname{div}\bigl(a(x,\nabla u)\bigr)+V(x) \vert x \vert ...
Yan Meng, Xianjiu Huang, Jianhua Chen
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Infinitely many solutions for Schrödinger–Newton equations
Communications in Contemporary Mathematics, 2023 We prove the existence of infinitely many non-radial positive solutions for the Schrödinger–Newton system [Formula: see text] provided that [Formula: see text] has the following behavior at infinity: [Formula: see text] where [Formula: see text] and [Formula: see text] are some positive constants.
Hu Y., Jevnikar A., Xie W.
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Infinitely many solutions for a gauged nonlinear Schrödinger equation with a perturbation
Nonlinear Analysis, 2021 In this paper, we use the Fountain theorem under the Cerami condition to study the gauged nonlinear Schrödinger equation with a perturbation in R2. Under some appropriate conditions, we obtain the existence of infinitely many high energy solutions for ...
Jiafa Xu, Jie Liu, Donal O'Regan
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Infinitely many non-radial solutions for a Choquard equation
Advances in Nonlinear Analysis, 2022 In this article, we consider the non-linear Choquard equation −Δu+V(∣x∣)u=∫R3∣u(y)∣2∣x−y∣dyuinR3,-\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\
Gao Fashun, Yang Minbo
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A sequence of positive solutions for sixth-order ordinary nonlinear differential problems
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Infinitely many solutions for a nonlinear sixth-order differential equation are obtained. The variational methods are adopted and an oscillating behaviour on the nonlinear term is required, avoiding any symmetry assumption.
Gabriele Bonanno, Roberto Livrea
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INFINITELY MANY SOLUTIONS FOR A NONLOCAL PROBLEM
Journal of Applied Analysis & Computation, 2020 Consider a class of nonlocal problems $ \left\{\begin{array}{lr} -\left(a-b \int_{\Omega}|\nabla u|^{2} d x\right) \Delta u=f(x, u), & x \in \Omega, \\ u=0, & x \in \partial \Omega, \end{array}\right.$ where $ a>0, b>0 $, $ \Omega\subset \mathbb{R}^N $ is a bounded open domain, $ f:\overline{\Omega} \times \mathbb R \longrightarrow \mathbb R $ is ...
Zhi-Yun Tang, Zeng-Qi Ou
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On a fractional differential equation with infinitely many solutions [PDF]
, 2012 We present a set of restrictions on the fractional differential equation $x^{(\alpha)}(t)=g(x(t))$, $t\geq0$, where $\alpha\in(0,1)$ and $g(0)=0$, that leads to the existence of an infinity of solutions starting from $x(0)=0$. The operator $x^{(\alpha)}$
Băleanu, Dumitru +2 more
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On Existence of Infinitely Many Homoclinic Solutions
Monatshefte f�r Mathematik, 2000 Using the concept of an isolating segment, some sufficient conditions for the existence of homoclinic solutions to nonautonomous ODEs are obtained. As an application it is shown that for all sufficiently small \(\varepsilon >0\) there exist infinitely many geometrically distinct solutions homoclinic to the trivial solution \(z=0\) to the equation ...
Wójcik, Klaudiusz, Zgliczyński, Piotr
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Infinitely many solutions for Hamiltonian systems
Journal of Differential Equations, 2002 AbstractWe consider two classes of the second-order Hamiltonian systems with symmetry. If the systems are asymptotically linear with resonance, we obtain infinitely many small-energy solutions by minimax technique. If the systems possess sign-changing potential, we also establish an existence theorem of infinitely many solutions by Morse theory.
Wenming Zou, Shujie Li
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Integrable subsystem of Yang--Mills dilaton theory [PDF]
, 2007 With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory coupled to the dilaton.
A Wereszczyński +7 more
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