Open AccessOn the existence of positive solutions for a nonlinear elliptic class of equations in R2 and R3
Author(s) -
José R. Quintero
Publication year - 2021
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v20i.9044
Subject(s) - mathematics , nonlinear system , compact space , mathematical analysis , homogeneous , type (biology) , elliptic curve , operator (biology) , elliptic operator , class (philosophy) , term (time) , pure mathematics , physics , quantum mechanics , ecology , biochemistry , chemistry , repressor , combinatorics , artificial intelligence , gene , transcription factor , computer science , biology
We study the existence of positive solutions for an elliptic equation in RN for N = 2, 3 which is related with the existence of standing (localized) waves and the existence of the ground state solutions for some physical model or systems in fluid mechanics to describe the evolution of weakly nonlinear water waves. We use a variational approach and the well-known principle of concentration-compactness due to P. Lions to obtain the existence of this type of solutions, even in the case that the nonlinear term g is a non-homogeneous function or an operator defined in H1(RN) with values in R.