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| In this paper, we deal with two types of degenerate coercive quasilinear elliptic equations, which are denoted by types I$_{dc}$ and II$_{dc}$, and two types of quasilinear elliptic equations with unbounded coefficients, which are denoted by types I$_{ub}$ and II$_{ub}$. An interesting phenomenon lies that although their principle parts (i.e., the second derivative term) are identical, their critical exponents are different. Moreover, for degenerate coercive cases, the critical exponents' difference I$_{dc}$$-$II$_{dc}$ is $ heta(2-2^*)$, while for the unbounded coefficients cases, the difference I$_{ub}$$-$II$_{ub}$ is $ heta(2^*-2)$. However, both the critical exponents' sums I$_{dc}$$+$I$_{ub}$ and II$_{dc}$$+$II$_{ub}$ are equal to $2(2^*-1)$. |
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| Keywords:Degenerate coercive ; critical exponents; unbounded coefficients |
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