Matrix elements in the $SU(1,1) \otimes SO(6)$ limit of the proton-neutron symplectic model
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DOI: 10.1088/1674-1137/ac1c67
Abstract: The matrix elements along the reduction chain Sp(12,R) \begin{document}$ \supset $\end{document} SU(1,1) \begin{document}$ \otimes $\end{document} SO(6) \begin{document}$ \supset $\end{document} U(1) \begin{document}$ \otimes $\end{document} SU \begin{document}$ _{pn} $\end{document} (3) \begin{document}$ \otimes $\end{document} SO(2) \begin{document}$ \supset $\end{document}… read more here.
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Positive solutions for quasilinear Schrödinger equations in $\mathbb{R}^N$
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DOI: 10.3934/cpaa.2017077
Abstract: In this article we study the following quasilinear Schrodinger equation \begin{document}$-Δ u+V(x)u-Δ(u^{2})u=g(u), x∈ \mathbb{R}^{N},$ \end{document} where \begin{document}$ V(x)$\end{document} tends to some limit \begin{document}$V_{∞}>0 $\end{document} as \begin{document}$|x|\to∞ $\end{document} and \begin{document}$g∈ C(\mathbb{R},\mathbb{R}) $\end{document} . We prove the… read more here.
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Liouville theorems for stable weak solutions of elliptic problems involving Grushin operator
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DOI: 10.3934/cpaa.2020025
Abstract: We consider the boundary value problem \begin{document}$\begin{equation*} \begin{cases} -{\rm div}_G(w_1\nabla_G u) = w_2f(u) &\text{ in } \Omega,\\ u=0 &\text{ on } \partial\Omega, \end{cases}\end{equation*}$ \end{document} where \begin{document}$\Omega$\end{document} is a bounded or unbounded \begin{document}$C^1$\end{document} domain of \begin{document}$\mathbb{R}^N$\end{document}… read more here.
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Bound state positive solutions for a class of elliptic system with Hartree nonlinearity
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DOI: 10.3934/cpaa.2020163
Abstract: In this paper, we are concerned with the following two-component system of Schrodinger equations with Hartree nonlinearity: \begin{document}$ \begin{equation*} \begin{cases} -\varepsilon ^{2}\Delta u+V_{1}\left( x\right) u+\lambda _{1}\left(I_{\varepsilon }\ast |u|^{p+1}\right)|u|^{p-1}u\\ \qquad\quad\; = \left(\mu _{1}|u|^{2p}+\beta(x) |u|^{q-1}|v|^{q+1}\right)u, & \text{in… read more here.
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Existence of infinitely many solutions for semilinear problems on exterior domains
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DOI: 10.3934/cpaa.2020193
Abstract: In this paper we prove the existence of infinitely many radial solutions of \begin{document}$ \Delta u + K(r)f(u) = 0 $\end{document} on the exterior of the ball of radius \begin{document}$ R>0 $\end{document} , \begin{document}$ B_{R}… read more here.
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On the strauss index of semilinear tricomi equation
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DOI: 10.3934/cpaa.2020213
Abstract: In our previous papers, we have given a systematic study on the global existence versus blowup problem for the small-data solution \begin{document}$ u $\end{document} of the multi-dimensional semilinear Tricomi equation \begin{document}$ \begin{equation*} \partial_t^2 u-t\, \Delta… read more here.
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Improved well-posedness results for the Maxwell-Klein-Gordon system in 2D
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DOI: 10.3934/cpaa.2021091
Abstract: The local well-posedness problem for the Maxwell-Klein-Gordon system in Coulomb gauge as well as Lorenz gauge is treated in two space dimensions for data with minimal regularity assumptions. In the classical case of data in… read more here.
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Classification of solutions to a nonlocal equation with doubly Hardy-Littlewood-Sobolev critical exponents
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DOI: 10.3934/dcds.2021074
Abstract: We consider the following nonlocal critical equation \begin{document}$\begin{equation} -\Delta u = (I_{\mu_1}\ast|u|^{2_{\mu_1}^\ast})|u|^{2_{\mu_1}^\ast-2}u +(I_{\mu_2}\ast|u|^{2_{\mu_2}^\ast})|u|^{2_{\mu_2}^\ast-2}u,\; x\in\mathbb{R}^N, \;\;\;\;\;\;\;(1) \end{equation}$ \end{document} where \begin{document}$ 0 if \begin{document}$ N = 3 $\end{document} or \begin{document}$ 4 $\end{document} , and \begin{document}$ N-4\leq\mu_1,\mu_2 if… read more here.
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On finite Morse index solutions of higher order fractional elliptic equations
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DOI: 10.3934/eect.2020081
Abstract: We consider sign-changing solutions of the equation \begin{document}$ (-{\Delta})^s u+\lambda u = |u|^{p-1}u \; \mbox{in}\; \mathbb R^n, $\end{document} where \begin{document}$ n\geq 1 $\end{document} , \begin{document}$ \lambda>0 $\end{document} , \begin{document}$ p>1 $\end{document} and \begin{document}$ 1 .… read more here.
Keywords: begin document; end document; finite morse; document begin ... See more keywords