Concentration of ground state solutions for critical generalized quasilinear equation with steep potential well
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DOI: 10.1002/mma.10334
Abstract: In this work, we are looking at the generalized quasilinear Schrödinger equations with critical growth and a steep potential well: −divg2(u)∇u+g(u)g′(u)|∇u|2+(λV(x)+1)u=|u|αp−2u+|u|α2∗−2u,x∈ℝN,$$ -\operatorname{div}\left({g}^2(u)\nabla u\right)+g(u){g}^{\prime }(u){\left|\nabla u\right|}^2+\left(\lambda V(x)+1\right)u={\left|u\right|}^{\alpha p-2}u+{\left|u\right|}^{\alpha {2}^{\ast }-2}u,\kern0.30em x\in {\mathrm{\mathbb{R}}}^N, $$ where λ>0,α∈[1,2],2 read more here.
Keywords: x0005e; steep potential; potential well; x0002b ... See more keywords
Existence of stable standing waves for the critical fractional Schrödinger equation with an inhomogeneous combined nonlinearity
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DOI: 10.1002/mma.10335
Abstract: We study the orbitally stability of standing waves for the L2$$ {L}^2 $$ ‐critical inhomogeneous combined source term fractional nonlinear Schrödinger equation: i∂tu−(−Δ)su+a|x|−b|u|pu+|u|4sNu=0,(t,x)∈ℝ×ℝN$$ i{\partial}_tu-{\left(-\Delta \right)}^su+a{\left|x\right|}^{-b}{\left|u\right|}^pu+{\left|u\right|}^{\frac{4s}{N}}u=0,\left(t,x\right)\in \mathrm{\mathbb{R}}\times {\mathrm{\mathbb{R}}}^N $$ where N2N−1 read more here.
Keywords: x0005e; schr dinger; inhomogeneous combined; dinger equation ... 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$$… read more here.
Keywords: x0005e; schr dinger; normalized ground; dinger systems ... See more keywords
Inverse Coefficient Problems for Dynamic Equations on Time Scales
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DOI: 10.1002/mma.10872
Abstract: In this article, we have worked toward developing the theory for the inverse coefficient problems on an arbitrary time scale. We considered a general n$$ n $$ th order linear dynamic equation yΔn(t)+∑i=1npi(t)yΔn−i(t)=f(t)$$ {y}^{\Delta^n}(t)+{\sum}_{i=1}^n{p}_i(t){y}^{\Delta^{n-i}}(t)=f(t) $$… read more here.
Keywords: x0005e; time; inverse coefficient; time scale ... See more keywords