Ahamed Adam Abdelgadir Mohammed

The boundary value problems of elliptic equations with critical growth have received significant attention in recent years due to the lack of compactness for Sobolev embedding in the critical case. This has brought a series of difficulties to the research.
The nonlinear elliptic problem with weight and singular coefficient is mainly sourced in physics, such as combustion theory. We improved the Sobolev-Hardy inequality and, using the improved Hardy inequality and Mountain Pass lemma without the Palais-Smale condition, we present the solution of singular biharmonic equation with sub-critical potential and critical exponent. By using the concentration compactness principle and mountain pass theorem respectively, we obtain existence results.