# Blow up of the solutions to a linear elliptic system involving Schr{\"o}dinger operators

## TL;DR

This paper investigates the blow-up behavior of solutions to a 2x2 linear elliptic system involving Schr{"o}dinger operators as a parameter approaches a critical eigenvalue, considering potentials with superquadratic growth.

## Contribution

It provides a detailed analysis of solution blow-up in a linear elliptic system with Schr{"o}dinger operators, including cases with double eigenvalues and superquadratic potentials.

## Key findings

- Solutions blow up as the parameter approaches the principal eigenvalue.
- The analysis covers systems with constant coefficient matrices and superquadratic potentials.
- The behavior is characterized near the critical eigenvalue.

## Abstract

We show how the solutions to a $2\times2$ linear system involving Schr{\"o}dinger operators blow up as the parameter $\mu$ tends to some critical value which is the principal eigenvalue of the system; here the potential is continuous positive with superquadratic growth and the square matrix of the system is with constant coefficients and may have a double eigenvalue.