# Mini-Max Algorithm via Pohozaev Manifold

## TL;DR

This paper introduces a novel algorithm that finds ground state solutions of certain nonlinear problems by minimizing the functional constrained to the Pohozaev manifold, offering a new approach to numerical solutions.

## Contribution

The paper proposes a new mini-max algorithm utilizing the Pohozaev manifold to efficiently compute ground state solutions for nonlinear problems.

## Key findings

- Successfully applied to find radially symmetric positive solutions
- Demonstrated effectiveness across various parameters
- Provides an alternative to traditional mini-max methods

## Abstract

A new algorithm for solving non-homogeneous asymptotically linear and superlinear problems is proposed. The ground state solution of the problem, which in general is obtained as a mini-max of the associated functional, is obtained as the minimum of the functional constrained to the Pohozaev manifold instead. Examples are given of the use of this method for finding numerical radially symmetric positive solutions depending on various parameters.