Multistability of fractional‐order Cohen–Grossberg neural networks with state‐dependent switching and time‐varying delays via Gaussian‐like activation functions
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DOI: 10.1002/asjc.3752
Abstract: This paper investigates the multistability of state‐dependent switched and time‐varying delayed fractional‐order Cohen–Grossberg neural networks (SFoCGNNs) by leveraging the geometric properties of a Gaussian‐like activation function (AF). Using the state‐space partition method and Brouwer's fixed… read more here.
Keywords: state dependent; amp x0005e; time varying; amp ... See more keywords
Weakly coupled systems of semilinear σ‐evolution equations with friction and visco‐elastic type damping
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DOI: 10.1002/mma.10473
Abstract: In the present paper, we are interested to study global (in time) existence of small data Sobolev solutions to the Cauchy problem for a weakly coupled system of two semilinear σk$$ {\sigma}_k $$ ‐evolution equations… read more here.
Keywords: x0005e; equations friction; weakly coupled; amp x0005e ... See more keywords
Normalized Ground States for Nonlinear Coupled SchröDinger Systems With Critical Exponential Growth in ℝ2
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DOI: 10.1002/mma.10772
Abstract: In this paper, we study the existence of normalized ground state solutions to the nonlinear Schrödinger systems with critical exponential growth nonlinearities and nonlinear coupled terms in ℝ2$$ {\mathbb{R}}^2 $$ satisfying the normalized constraints ∫ℝ2u2=a$$… read more here.
Keywords: x0005e; schr dinger; normalized ground; dinger systems ... See more keywords
A Class of Pseudo‐Differential Operators Involving the Weinstein Transform
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DOI: 10.1002/mma.11163
Abstract: In this paper, the authors introduce and investigate a certain family of pseudo‐differential operators which is associated with the symbol class Sωr$$ {S}_{\omega}^r $$ on the space Sωℝ+n+1$$ {S}_{\omega}\left({\mathbb{R}}_{+}^{n+1}\right) $$ for a real‐valued convex function… read more here.
Keywords: weinstein transform; class; amp x0005e; differential ... See more keywords
Elliptic System With Sublinear Signal Production in Dimension 2
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DOI: 10.1002/mma.70140
Abstract: We consider the nonlinear elliptic system u∈W01,q(Ω):−div(M(x)∇u)+u=−div(uM(x)∇ψ)+f(x),ψ∈W01,2(Ω):−div(M(x)∇ψ)=Φ(u),$$ {\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