Abstract
In this manuscript, we study a Robin problem driven by the p(x)-Laplacian with two parameters. -div(vertical bar del w vertical bar(p(x)-2)del w) = lambda V(x)vertical bar w vertical bar(q(x)-2)w, x is an element of Q, vertical bar del w vertical bar(P(x)-2)partial derivative w/partial derivative n + theta(x)vertical bar w vertical bar(p(x)-2) = beta V-1(x)vertical bar w vertical bar(r(x)-2)w. x is an element of partial derivative Q. Here, Q is a regular bounded domain in R-N, lambda, beta > 0, p, q are continuous functions on (Q) over bar, partial derivative w/partial derivative n is the outer unit normal derivative on partial derivative Q, theta is an element of L-infinity (partial derivative Q), such that ess inf(x is an element of partial derivative Q) theta(x) > 0, V is an indefinite function in L-s(x) (Q) and V-1 is a non-negative one in L-s1(x) (partial derivative Q). Using variational tools, we show the existence of a non-trivial solution.