I have some questions about Karush Kuhn Tucker conditions. I am not clear about the theory. There are plenty of theorems and I am confused with it. Let us say we have the following problem: We have a general problem, not a convex problem. $$\min f(x)\\g_{j}(x)\le 0,\forall j\in J\\h_{k}(x)=0,\forall k \in K. $$ I will solve it.....Lagrange function, verifying primal feasibility, dual feasibility and complementary slackness and I will get some KKT points.
If I get no KKT point, can I say that the problem has no solution or what is the conclusion?
In answer to your first question: You can't conclude anything without making additional assumptions about the regularity of the problem- these assumptions are called "constraint qualifications."
For example, the problem
$\min x_{2}$
subject to
$(x_{1}-1)^{2}+x_{2}^{2}=1$
$(x_{1}+1)^{2}+x_{2}^{2}=1$
has only one feasible solution at $x_{1}=0$, $x_{2}=0$, but this point doesn't satisfy the KKT conditions. Thus there are no KKT points but $x_{1}=0$, $x_{2}=0$ is the unique optimal solution to the problem.