We study the following Schr?dinger equation with variable exponent−Δu+u=u^(p+∈a)(x),u>0 in R^(N),where∈>0,1<p<N+2/N−2,a(x)∈C^(1)(R^(N))∩L^(∞)(R^(N)),N≥3.Under certain assumptions on a vector field r...We study the following Schr?dinger equation with variable exponent−Δu+u=u^(p+∈a)(x),u>0 in R^(N),where∈>0,1<p<N+2/N−2,a(x)∈C^(1)(R^(N))∩L^(∞)(R^(N)),N≥3.Under certain assumptions on a vector field related to a(x),we use the Lyapunov–Schmidt reduction to show the existence of single peak solutions to the above problem.We also obtain local uniqueness and exact multiplicity results for this problem by the Pohozaev type identity.展开更多
基金National Natural Science Foundation of China(Grant Nos.11971147 and12371111)The second author is partially supported by National Natural Science Foundation of China(Grant No.11831009)+1 种基金the Fundamental Research Funds for the Central Universities(Grant Nos.KJ02072020-0319,CCNU22LJ002)The third author is supported by National Natural Science Foundation of China(Grant No.12201232)。
文摘We study the following Schr?dinger equation with variable exponent−Δu+u=u^(p+∈a)(x),u>0 in R^(N),where∈>0,1<p<N+2/N−2,a(x)∈C^(1)(R^(N))∩L^(∞)(R^(N)),N≥3.Under certain assumptions on a vector field related to a(x),we use the Lyapunov–Schmidt reduction to show the existence of single peak solutions to the above problem.We also obtain local uniqueness and exact multiplicity results for this problem by the Pohozaev type identity.
