I wonder if there are theories on elliptic operator $$Lu=\Delta u + b_iu_i + cu$$ when $c>0$, when $c<0$, we are glad to have maximum principle, so the bijectivity can be easily analyzed, but I hardly found any theories on it except the Fredholm alternative theorem. Could you share with me some studies on it if you know some?

I wonder if there are theories on elliptic operator $$Lu=\Delta u + b_iu_i + cu$$ when $c>0$, when $c<0$, we are glad to have maximum principle, so the bijectivity can be easily analyzed, but I hardly found any theories on $c>0$ case except the Fredholm alternative theorem which stated that either $$Lu=f$$ has a unique solution so bijective or $$Lu=0$$ has non-trivial solution so not injective. Could you share with me some studies on it if you know something else?

I wonder if there are theories on ellipti operator $$Lu=\Delta u + b_iu_i + cu$$ when $c>0$, when $c<0$, we are glad to have maximum principle, so the bijectivity can be easily analyzed, but I hardly found any theories on it except the Fredholm alternative theorem. Could you share with me some studies on it if you know some?

I wonder if there are theories on elliptic operator $$Lu=\Delta u + b_iu_i + cu$$ when $c>0$, when $c<0$, we are glad to have maximum principle, so the bijectivity can be easily analyzed, but I hardly found any theories on it except the Fredholm alternative theorem. Could you share with me some studies on it if you know some?