Ground state solutions for asymptotically linear Schrödinger equations on locally finite graphs
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DOI: 10.1002/mma.10145
Abstract: We are considered with the following nonlinear Schrödinger equation: −Δu+(λa(x)+1)u=f(u),x∈V,$$ -\Delta u+\left(\lambda a(x)+1\right)u=f(u),x\in V, $$ on a locally finite graph G=(V,E)$$ G=\left(V,E\right) $$ , where V$$ V $$ denotes the vertex set, E$$ E $$… read more here.
Keywords: schr dinger; asymptotically linear; state; ground state ... See more keywords
Periodic Solutions of Asymptotically Linear Autonomous Hamiltonian Systems with Resonance
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DOI: 10.1007/s10884-017-9608-0
Abstract: In this paper we define the index at infinity of an asymptotically linear autonomous Hamiltonian system. We use this index to prove the existence and bifurcation from infinity of periodic solutions of the system. We… read more here.
Keywords: periodic solutions; asymptotically linear; linear autonomous; solutions asymptotically ... See more keywords
Ground State Solutions of Discrete Asymptotically Linear Schrödinger Equations with Bounded and Non-periodic Potentials
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DOI: 10.1007/s10884-019-09743-4
Abstract: We study the existence of ground state solutions for a class of discrete nonlinear Schrödinger equations with a sign-changing potential V that converges at infinity and a nonlinear term being asymptotically linear at infinity. The… read more here.
Keywords: asymptotically linear; schr dinger; ground state; ground ... See more keywords
Sign-Changing Solutions for Chern–Simons–Schrödinger Equations with Asymptotically 5-Linear Nonlinearity
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DOI: 10.1007/s40840-020-00974-z
Abstract: In this paper, we study the following Chern–Simons–Schrodinger equation $$\begin{aligned} {\left\{ \begin{array}{ll} \displaystyle -\Delta u+\omega u+\lambda \Big (\frac{h^{2}(|x|)}{|x|^{2}}+ \int _{|x|}^{+\infty }\frac{h(s)}{s}u^{2}(s)\hbox {d}s\Big )u=g(u) \quad \text{ in }\ {\mathbb {R}}^{2},\\ \displaystyle u\in H_r^1({\mathbb {R}}^{2}), \end{array}\right. }… read more here.
Keywords: changing solutions; chern simons; solutions chern; asymptotically linear ... See more keywords
Multiple nodal solutions for Choquard type equations with an asymptotically linear term
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DOI: 10.1080/00036811.2025.2496284
Abstract: In this paper, we consider the following Choquard type equation with an asymptotically linear term (1) $$\begin{align} -\Delta u+u=\left(\int_{\mathbb{R}^N}\frac{|u(y)|^p}{|x-y|^{N-\alpha}}\,{\rm d}y\right)|u|^{p-2}u+f(u) \end{align}$$−Δu+u=(∫RN|u(y)|p|x−y|N−αdy)|u|p−2u+f(u) where $ N\geq 3, \alpha \in (N-4,N), p\in (2,\frac {N+\alpha }{N-2}) $ N≥3,α∈(N−4,N),p∈(2,N+αN−2) and… read more here.
Keywords: asymptotically linear; multiple nodal; linear term; nodal solutions ... See more keywords