On the uniqueness of bound state solutions of a semilinear equation with\n weights

2018/09/20 by Carmen Cortázar, Cortazar, Carmen, Marta García‐Huidobro +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1809.07711

openalex publication_date 2018/09/20 · openalex created_date 2022/08/03 · openalex updated_date 2026/07/28

Abstract

We consider radial solutions of a general elliptic equation involving a\nweighted Laplace operator. We establish the uniqueness of the radial bound\nstate solutions to div
big(
mathsf A
,
nabla v
big)+
mathsf\nB
,f(v)=0
,,
quad
lim_{|x|
to+
infty}v(x)=0,
quad x
in
mathbb Rⁿ, n>2,\nwhere mathsf A and mathsf B are two positive, radial, smooth functions\ndefined on mathbb Rⁿ\∖ 0 .\n We assume that the nonlinearity f\∈ C(-c,c), 0<c\≤\∞ is an odd\nfunction satisfying some convexity and growth conditions, and has a zero at\nb>0, is non positive and not identically 0 in (0,b), positive in (b,c),\nand is differentiable in (0,c).\n

Related

• Multiplicity results for bound state solutions of a semilinear equation
• Uniqueness results for semilinear elliptic systems on \Rⁿ
• On the radial solutions of a system with weights under the\n Keller--Osserman condition
• A new approach to the study of elliptic semilinear equations
• On the uniqueness of solutions of a semilinear equation in an annulus