We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavio...We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).展开更多
This paper is devoted to the following fractional relativistic Schrödinger equation:(−Δ+m2)^(s)u+V(x)u=f(x,u),x∈R^(N).where(−Δ+m2)^(s)is the fractional relativistic Schrödinger operator,s∈(0,1),m>0,V:...This paper is devoted to the following fractional relativistic Schrödinger equation:(−Δ+m2)^(s)u+V(x)u=f(x,u),x∈R^(N).where(−Δ+m2)^(s)is the fractional relativistic Schrödinger operator,s∈(0,1),m>0,V:ℝ^(N)→ℝis a continuous potential and f:ℝ^(N)×ℝ→ℝis a superlinear continuous nonlinearity with subcritical growth.We consider the case where the potential V is indefinite so that the relativistic Schrödinger operator(−Δ+m2)s+V possesses a finite-dimensional negative space.With the help of extension method and Morse theory,the existence of a nontrivial solution for the above problem is obtained.展开更多
基金supported by Piano della Ricerca di Ateneo 2020-2022-PIACERIProject MO.S.A.I.C"Monitoraggio satellitare,modellazioni matematiche e soluzioni architettoniche e urbane per lo studio,la previsione e la mitigazione delle isole di calore urbano",Project EEEP&DLaD.S。
文摘We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).
基金supported by National Natural Science Foundation of China(No.12161038)Natural Science Foundation Program of Jiangxi Provincial(No.20232BABL201009)Science and Technology Project of Jiangxi provincial Department of Education(No.GJJ212204,GJJ2200635).
文摘This paper is devoted to the following fractional relativistic Schrödinger equation:(−Δ+m2)^(s)u+V(x)u=f(x,u),x∈R^(N).where(−Δ+m2)^(s)is the fractional relativistic Schrödinger operator,s∈(0,1),m>0,V:ℝ^(N)→ℝis a continuous potential and f:ℝ^(N)×ℝ→ℝis a superlinear continuous nonlinearity with subcritical growth.We consider the case where the potential V is indefinite so that the relativistic Schrödinger operator(−Δ+m2)s+V possesses a finite-dimensional negative space.With the help of extension method and Morse theory,the existence of a nontrivial solution for the above problem is obtained.
