Elliptic System With Sublinear Signal Production in Dimension 2
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DOI: 10.1002/mma.70140
Abstract: We consider the nonlinear elliptic system u∈W01,q(Ω):−div(M(x)∇u)+u=−div(uM(x)∇ψ)+f(x),ψ∈W01,2(Ω):−div(M(x)∇ψ)=Φ(u),$$ {\displaystyle \begin{array}{ll}u\in {W}_0^{1,q}\left(\Omega \right):& -\operatorname{div}\left(M(x)\nabla u\right)+u=-\operatorname{div}\left(u\kern0.3em M(x)\kern0.3em \nabla \psi \right)+f(x),\\ {}\psi \in {W}_0^{1,2}\left(\Omega \right):& -\operatorname{div}\left(M(x)\nabla \psi \right)=\Phi (u),\end{array}} $$ where Ω$$ \Omega $$ is a bounded, open subset… read more here.
Keywords: amp; amp x0005e; right amp; div ... See more keywords
Semiclassical states for fractional Schrödinger equations with critical nonlinearities
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DOI: 10.1002/mma.9747
Abstract: In this paper, we consider the following fractional Schrödinger equation ε2s(−Δ)su+V(x)u=P(x)f(u)+Q(x)|u|2s∗−2uinℝN,$$ {\varepsilon}^{2s}{\left(-\Delta \right)}^su+V(x)u=P(x)f(u)+Q(x){\left|u\right|}^{2_s^{\ast }-2}u\kern0.30em \mathrm{in}\kern0.4em {\mathrm{\mathbb{R}}}^N, $$ where ε>0$$ \varepsilon >0 $$ is a parameter, s∈(0,1),2s∗=2NN−2s,N>2s,(−Δ)s$$ s\in \left(0,1\right),{2}_s^{\ast }=\frac{2N}{N-2s},N>2s,{\left(-\Delta \right)}^s $$ is the fractional Laplacian… read more here.
Keywords: schr dinger; amp; amp x0005e; fractional schr ... See more keywords