6533b7ddfe1ef96bd1275252

RESEARCH PRODUCT

Elliptic equations involving the $1$-Laplacian and a subcritical source term

Alexis Molino SalasSergio Segura De León

subject

Dirichlet problemApplied Mathematics010102 general mathematicsMathematics::Analysis of PDEsType (model theory)01 natural sciencesTerm (time)010101 applied mathematicsElliptic curveIdentity (mathematics)Operator (computer programming)Mathematics - Analysis of PDEsBounded functionFOS: MathematicsApplied mathematics0101 mathematicsLaplace operator35J75 35J20 35J92AnalysisAnalysis of PDEs (math.AP)Mathematics

description

In this paper we deal with a Dirichlet problem for an elliptic equation involving the $1$-Laplacian operator and a source term. We prove that, when the growth of the source is subcritical, there exist two bounded nontrivial solutions to our problem. Moreover, a Pohozaev type identity is proved, which holds even when the growth is supercritical. We also show explicit examples of our results.

yearjournalcountryeditionlanguage
2017-07-06
http://arxiv.org/abs/1707.01934