THE EXISTENCE OF WEAK SOLUTION FOR DEGENERATE Sigma Delta(pi(x))-EQUATION
Using variational methods, we establish the existence of non-trivial solution for the following generalized class of p(x)-Laplacian [GRAPHICS] where Omega is a bounded domain in R-N with smooth boundary partial derivative Omega, p(i),q(j) is an element of C((Omega) over bar), and f is a caratheodory function with some adequate assumptions. Also, we show that if we replace Omega by R-N in Problem (P), the generate equation has a weak solution. Finally, it is shown that with some adequate assumptions on f, the Problem (P) has two sequences of solution.
weak solution compact embedding weak convergent p(.)- laplacian variable exponent sobolev space critical point palais-smale condition mountain pass theorem