MULTIPLICITY RESULTS FOR A NONLINEAR ROBIN PROBLEM WITH VARIABLE EXPONENT

作者：Saiedinezhad Somayeh^*; Radulescu Vicentiu D

来源：Journal of Nonlinear and Convex Analysis, 2016, 17(8): 1567-1582.

• p(.)-Laplacian
• variable exponent Sobolev space
• symmetric mountain pass theorem
• Fountain theorem
• Ekeland variational principle
• Ljusternik-Schnirelmann principle

The nonlinear weighted Robin problem
{-div (a(x)vertical bar del u vertical bar(p(x)-2)del u) + b(x)vertical bar u vertical bar(q(x)-2)u(x)
-lambda c(x)vertical bar u vertical bar(r(x)-2)u(x) = f(x,u); in Omega,
vertical bar del u vertical bar(p(x)-2) partial derivative u/partial derivative v + beta(x)vertical bar del u vertical bar(p(x)-2)u = 0, on partial derivative Omega
is studied in the present paper. We are concerned with maximum or minimum growth of the corresponding energy functional by various conditions on p, q, r. We also obtain qualitative properties about the behavior of energy functional and, by applying some variational methods, several existence results for the sequence of weak solutions are deduced. Finally, we study our problem by modeling as a nonlinear eigenvalue problem.

• 出版日期2016