We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of ...We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.展开更多
In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sig...In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sign and satisfy some additional conditions;u∈H_(A)^(1)(R^(N))and A:R^(N)→R^(N) is a magnetic potential.Also using the Nehari method in combination with other complementary arguments,we discuss the existence of infinitely many solutions to the problem in question,varying the assumptions about the weight functions.展开更多
文摘We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.
基金grants from FAPESP 2017/16108-6grants from FAPESP 2019/24901-3 and CNPq 307061/2018-3supported by CAPES/Brazil and the paper was completed while the second author was visiting the Departament of Mathematics of UFJF whose hospitality she gratefully acknowledges.
文摘In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2<q<p<2^(∗)=2N/N−2,a(x)and b(x)are functions that can change sign and satisfy some additional conditions;u∈H_(A)^(1)(R^(N))and A:R^(N)→R^(N) is a magnetic potential.Also using the Nehari method in combination with other complementary arguments,we discuss the existence of infinitely many solutions to the problem in question,varying the assumptions about the weight functions.
