We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The ex...We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥ 2p.展开更多
We study the following mean field equation■,whereρis a real parameter.We obtain the existence of multiple non-axially symmetric solutions bifurcating from u=0 at the valuesρ=4 n(n+1)πfor any odd integer n≥3.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101134, 11371128） and the Young Teachers Program of Hunan University. The authors thank the anonymous referees for their valuable comments and suggestions.
文摘We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p 〉 2, -△p^u -= f（u） in R^2m for all dimensions satisfying 2m ≥ p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥ 2p.
基金supported by the Natural Science Foundation of Hunan ProvinceChina(Grant No.2016JJ2018)+1 种基金partially supported by NSF grants DMS-1601885 and DMS-1901914Simons Foundation Award 617072。
文摘We study the following mean field equation■,whereρis a real parameter.We obtain the existence of multiple non-axially symmetric solutions bifurcating from u=0 at the valuesρ=4 n(n+1)πfor any odd integer n≥3.
