Existence and concentration of ground states for a Choquard equation with competing potentials
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DOI: 10.1016/j.jmaa.2018.04.065
Abstract: Abstract In this paper, we are concerned with the following Choquard equation in R 3 that − ϵ 2 Δ u + V ( x ) u = ϵ μ − 3 [ ( ∫… read more here.
Keywords: ground states; existence concentration; ground; choquard equation ... See more keywords
EXISTENCE AND CONCENTRATION OF SOLUTION FOR A NON-LOCAL REGIONAL SCHRÖDINGER EQUATION WITH COMPETING POTENTIALS
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DOI: 10.1017/s0017089518000289
Abstract: Abstract In this paper, we study the existence and concentration phenomena of solutions for the following non-local regional Schrödinger equation $$\begin{equation*} \left\{ \begin{array}{l} \epsilon^{2\alpha}(-\Delta)_\rho^{\alpha} u + Q(x)u = K(x)|u|^{p-1}u,\;\;\mbox{in}\;\; \mathbb{R}^n,\\ u\in H^{\alpha}(\mathbb{R}^n) \end{array} \right. \end{equation*}$$… read more here.
Keywords: local regional; non local; regional schr; existence concentration ... See more keywords
Existence and concentration of ground state solution to a nonlocal Schrödinger equation
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DOI: 10.1063/5.0008911
Abstract: We study a class of Schrodinger–Kirchhoff system involving a critical exponent. We aim to find suitable conditions to assure the existence of a positive ground state solution of Nehari–Pohozaev type ue with exponential decay at… read more here.
Keywords: existence concentration; ground state; state solution;
Existence and concentration of positive solutions for a class of discontinuous quasilinear Schrödinger problems in $\mathbb{R}^{N}$
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DOI: 10.1186/s13661-020-01362-z
Abstract: In this paper, a class of quasilinear Schrodinger equations with discontinuous nonlinearity is considered. After changing variables, by using nonsmooth critical point theory, we obtain the existence and concentration of positive solutions for this problem… read more here.
Keywords: solutions class; existence concentration; positive solutions; concentration positive ... See more keywords
Existence and concentration of solutions for nonautomous Schrödinger–Poisson systems with critical growth
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DOI: 10.14232/ejqtde.2017.1.88
Abstract: In this paper, we study the following Schrödinger–Poisson system { −∆u + u + μφu = λ f (x, u) + u5 in R3, −∆φ = μu2 in R3, where μ, λ > 0 are… read more here.
Keywords: existence concentration; concentration solutions; schr dinger; dinger poisson ... See more keywords
The existence and concentration behavior of ground state solutions for fractional Schrödinger–Kirchhoff type equations
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DOI: 10.5186/aasfm.2018.4361
Abstract: In this paper, we study the following fractional Schrödinger Kirchhoff type problem (Qǫ) { Lǫu = K(x)f(u) in R , u ∈ H(R), where Lǫ is a nonlocal operator defined by L s ǫu =… read more here.
Keywords: dinger kirchhoff; fractional schr; existence concentration; schr dinger ... See more keywords