| In this thesis, we are concerned with the comparison principle for a class of quasi-linear elliptic equations which is particularly useful in dealing with boundary blow-up problems.Suppose that D is a bounded smooth domain in RN, p>1,0<m<p-1, a(x) and β(x) are non-negative continuous functions on D with‖α‖L∞(D)<oo and β(x)(?)0for x∈D, g(s)∈C([0,∞)) and satisfies Let u1, u2∈C1(D) be positive in D and satisfy in the sense of distributions-△pu1-a(x)u1m=β(x)g(u1)≥0≥-△pu2-a(x)u2m+β(x)g(u2), and Then u1≥2in D.Then, we use the comparison principle to prove the existence of a positive boundary blow-up solution for the following equation-△pu=(?)(x)um-φ(x)uq, x∈Ω., where0<m<p-1<q.(0.1)Finally, we summarized several comparison principles with p-Laplacian oper-ator and their applications in order to understand the development of comparison principles with p-Laplacian operator well. |
