Eigenvalue Problem For A Class Of Nonlinear Operators In A Variable Exponent Sobolev Space
Keywords:
eigenvalue problem, p(·)-Laplacian, mean curvature operator, mixed boundary value problem, variable exponent Sobolev spaceAbstract
In this paper, we consider an eigenvalue problem for a class of nonlinear operators containing p(·)-Laplacian and mean curvature operator with mixed boundary conditions. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show that the eigenvalue problem has an infinitely many eigenpairs by using the Ljusternik-Schnirelmann principle of the calculus of variation. Moreover, in a variable exponent
Sobolev space, we derive some sufficient conditions that the infimum of all eigenvalues is equal to zero and remains to positive, respectively.
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