We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1<p<q<N,α<q,1<α≤p∗q′/p′with p∗=NpN−p,ϕ(t)behaves like ...We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1<p<q<N,α<q,1<α≤p∗q′/p′with p∗=NpN−p,ϕ(t)behaves like t q/2 for small t and t p/2 for large t,and p′and q′are the conjugate exponents of p and q,respectively.We study the existence of nontrivial radially symmetric solutions for the problem above by applying the mountain pass theorem and the fountain theorem.Moreover,taking into account the dual fountain theorem,we show that the problem admits a sequence of small-energy,radially symmetric solutions.展开更多
基金the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(NRF-2019R1F1A1057775)Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(2018R1D1A1B07048620).
文摘We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1<p<q<N,α<q,1<α≤p∗q′/p′with p∗=NpN−p,ϕ(t)behaves like t q/2 for small t and t p/2 for large t,and p′and q′are the conjugate exponents of p and q,respectively.We study the existence of nontrivial radially symmetric solutions for the problem above by applying the mountain pass theorem and the fountain theorem.Moreover,taking into account the dual fountain theorem,we show that the problem admits a sequence of small-energy,radially symmetric solutions.
