We have these two nonlinear inequalities (I): $$x^2+y^2>0$$ $$3x^2+3y^2-4y^6>0$$ We want to represent this problem as a Linear Matrix Inequality Problem, i.e, we want to derive a positive definite matrix A such that $A>0$ implies (I)
1- How to solve this particular problem?
2- What is the general method of solving these problems?
*note: I've tried Schur lemma with no avail