Existence Of Positive Solution For A Class Of Quasilinear Elliptic Equations

In this paper ,we use topological degree method to study the existence of positive solutions for a class of quasilinear elliptic equations as follow:where (p(x) > 1) is p(x)-Laplacian equation , Ω is bounded domain in R~N with smooth boundary It, is well known that in the R~N ,the P-Laplacian equations problems have been studied by many authors in nation and overseas.see[2][4][5] But from the method aspect,many authors study these problems by using Mountain pass theorem,Critical point theory,Strong maximum principle Or Morse theory.First.we will study existence of positive solutions for the following class of p-Laplacian quasilinear elliptic equations in chapter 2 by using the topological degree argument :Next,In chapter 3,for further argument,we study strong maximum principle for a class of p(x)-Laplacian equations such as:This result extends the result of Professor Fan xian ling for the right term f(x,u) = 0 to generality.In chapter 4,we study the positve solution of above p(x)-Laplacian problem by usingtopological degree method and we can find that using topological degree method is more valid than the other meathod.