On the existence of positive solutions for a nonlinear elliptic class of equations in R2 and R3

Authors

  • Jose Quintero Mathematics Department, Science Faculty, Universidad del Valle, Colombia

DOI:

https://doi.org/10.24297/jam.v20i.9044

Keywords:

variational approach, concentration-compactness, Elliptic equation

Abstract

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.

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References

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Published

2021-06-04

How to Cite

Quintero, J. (2021). On the existence of positive solutions for a nonlinear elliptic class of equations in R2 and R3. JOURNAL OF ADVANCES IN MATHEMATICS, 20, 188–210. https://doi.org/10.24297/jam.v20i.9044

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