Infinitely Many Positive Nonradial Solutions for the Kirchhoff Equation
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DOI: 10.1002/mma.10718
Abstract: We are concerned with the existence of positive nonradial solutions to the following Kirchhoff equation: −a+b∫ℝ3|∇u|2dxΔu+V(|x|)u=Q(|x|)|u|p−1u,x∈ℝ3,$$ -\left(a+b{\int}_{{\mathbb{R}}^3}{\left|\nabla u\right|}^2 dx\right)\Delta u+V\left(|x|\right)u=Q\left(|x|\right){\left|u\right|}^{p-1}u,\kern1em x\in {\mathbb{R}}^3, $$ where a,b>0,10$$ {V}_0,{Q}_0,\theta, \kappa, {d}_1>0 $$ and d2∈ℝ$$ {d}_2\in \mathbb{R} $$ .… read more here.
Keywords: many positive; nonradial solutions; infinitely many; kirchhoff equation ... See more keywords
The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function
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DOI: 10.2989/16073606.2017.1396508
Abstract: Abstract In the paper, by the Cauchy integral formula in the theory of complex functions, an integral representation for the reciprocal of the weighted geometric mean of many positive numbers is established. As a result,… read more here.
Keywords: positive numbers; reciprocal weighted; many positive; geometric mean ... See more keywords