科研之友
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摘要
We consider a class of generalized quasilinear Schrodinger equations @@@ -Delta u - gamma Delta l(u(2))l'(u(2))u + lambda u = vertical bar u vertical bar(p-2)u, x is an element of R-N, @@@ where gamma is a parameter, lambda > 0, p > 2, N >= 3, l is the real function. Under mild conditions posed on l and without sign constraints on gamma, we establish a positive classical solution u(gamma) if vertical bar gamma vertical bar is small. Moreover, the asymptotic behavior of u(gamma) as gamma -> 0 is investigated.
