Existence of Ground State Solutions for Fractional Schrödinger–Poisson Systems with Doubly Critical Growth
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DOI: 10.1007/s00009-020-01660-x
Abstract: This paper considers a class of fractional Schrodinger–Poisson type systems with doubly critical growth $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^su+V(x)u-\phi |u|^{2^*_s-3}u=K(x)|u|^{2^*_s-2}u,&{} \text{ in } {\mathbb {R}}^3,\\ (-\Delta )^s\phi =|u|^{2^*_s-1},&{} \text{ in } {\mathbb {R}}^3, \end{array}\right. \end{aligned}$$… read more here.
Keywords: ground state; systems doubly; doubly critical; state solutions ... See more keywords
Three solutions for a nonlocal problem with critical growth
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DOI: 10.1016/j.jmaa.2018.09.038
Abstract: The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation $(-\Delta_p)^s u= |u|^{p^{*}_s -2} u +\lambda f(x,u)$ in… read more here.
Keywords: three solutions; solutions nonlocal; nonlocal problem; critical growth ... See more keywords
Bifurcations of radially symmetric solutions in a coupled elliptic system with critical growth in Rd for d = 3,4
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DOI: 10.1016/j.jmaa.2019.123726
Abstract: Abstract We consider a system of coupled elliptic partial differential equations with critical growth in R d for d = 3 , 4 and study bifurcations of three families of radially symmetric, bounded solutions. We… read more here.
Keywords: system; critical growth; radially symmetric; three families ... See more keywords
Concentration phenomenon of solutions for a class of Kirchhoff-type equations with critical growth
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DOI: 10.1016/j.jmaa.2020.124355
Abstract: Abstract In this paper, we study the following Kirchhoff-type equations with critical growth − ( e 2 a + e b ∫ R 3 | ∇ u | 2 d x ) Δ u +… read more here.
Keywords: critical growth; equations critical; kirchhoff type; type equations ... See more keywords
Ground state and nodal solutions for a Schrödinger-Poisson equation with critical growth
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DOI: 10.1063/1.5050856
Abstract: In this paper, we study a nonlinear Schrodinger-Poisson equation with critical growth in R3. Under some assumptions on potential functions, we prove that for p ∈ (3, 6), the Schrodinger-Poisson equation has ground state and… read more here.
Keywords: poisson equation; state nodal; critical growth; equation critical ... See more keywords
On the least energy solutions for semilinear Schrödinger equation with electromagnetic fields involving critical growth and indefinite potentials
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DOI: 10.1080/00036811.2017.1359559
Abstract: Abstract In this paper, we are concerned with the following semilinear Schrödinger equation with electromagnetic fields and critical growth for sufficiently large , where , and its zero set is not empty, is the critical… read more here.
Keywords: dinger equation; electromagnetic fields; critical growth; equation ... See more keywords
Ground state solution for a class of Schrödinger equations involving general critical growth term
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DOI: 10.1088/1361-6544/aa5659
Abstract: In this paper, we study a class of Schrodinger equations −u=k(u),x∈RN, where and k satisfies very general critical growth conditions. By using the Pohozaev constraint, we obtain a positive ground state solution which is radially… read more here.
Keywords: state solution; general critical; class; critical growth ... See more keywords
Multiplicity and Concentration Results for a Magnetic Schrödinger Equation With Exponential Critical Growth in ℝ2
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DOI: 10.1093/imrn/rnaa074
Abstract: In this paper we study the following nonlinear Schrödinger equation with magnetic field $$\begin{align*} \left(\frac{\varepsilon}{i}\nabla-A(x)\right)^{2}u+V(x)u=f(| u|^{2})u,\quad x\in\mathbb{R}^{2}, \end{align*}$$where $\varepsilon>0$ is a parameter, $V:\mathbb{R}^{2}\rightarrow \mathbb{R}$ and $A: \mathbb{R}^{2}\rightarrow \mathbb{R}^{2}$ are continuous potentials, and $f:\mathbb{R}\rightarrow \mathbb{R}$ has… read more here.
Keywords: dinger equation; critical growth; exponential critical; multiplicity concentration ... See more keywords
Existence of multiple positive solutions for fractional Laplace problems with critical growth and sign-changing weight in non-contractible domains
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DOI: 10.1186/s13661-019-1193-1
Abstract: We prove the existence of multiple positive solutions for a fractional Laplace problem with critical growth and sign-changing weight in non-contractible domains. read more here.
Keywords: solutions fractional; fractional laplace; positive solutions; critical growth ... See more keywords
Ground states for Kirchhoff-type equations with critical growth
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DOI: 10.3934/cpaa.2018124
Abstract: In this paper, we study the following Kirchhoff-type equation with critical growth \begin{document}$-(a+b\int {_{\mathbb{R}^3}} |\nabla u|^2dx)\triangle u+V(x)u = λ f(x,u)+|u|^4u, \; x \; ∈\mathbb{R}^3,$ \end{document} where a>0, b>0, λ>0 and f is a continuous superlinear… read more here.
Keywords: ground; critical growth; ground states; document ... See more keywords