Existence Results for a Nonlocal Problem Involving the p-Laplace Operator
نویسنده
چکیده
The present paper deals with a nonlocal problem under homogeneous Dirichlet boundary conditions, set in a bounded smooth domain Ω of R . The problem studied is a stationary version of the original Kirchhoff equation involving the p-Laplace operator. The question of the existence of weak solutions is treated. Using variational approach and applying the Mountain Pass Theorem together with Fountain theorem, the existence and multiplicity of solutions is obtained in the Sobolev space W 1,p (Ω).
منابع مشابه
Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator
The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.
متن کاملExistence of Weak Solutions for a Nonlocal Problem Involving the p(x)-Laplace Operator
This paper deals with the existence of weak solutions for some nonlocal problem involving the p (x)Laplace operator. Using a direct variational method and the theory of the variable exponent Sobolev spaces, we set some conditions that ensures the existence of nontrivial weak solutions.
متن کاملExistence of three positive solutions for nonsmooth functional involving the p-biharmonic operator
This paper is concerned with the study of the existence of positive solutions for a Navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. The existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. Our resul...
متن کاملOn nonlocal quasilinear equations and their local limits
We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal versions of p-Laplace, ∞-Laplace, mean curvature of graph, and even strongly degenerate operators. Our main results are non-trivial comparison, uniqueness, and existence results fo...
متن کاملInfinitely Many Solutions for a Steklov Problem Involving the p(x)-Laplacian Operator
By using variational methods and critical point theory for smooth functionals defined on a reflexive Banach space, we establish the existence of infinitely many weak solutions for a Steklov problem involving the p(x)-Laplacian depending on two parameters. We also give some corollaries and applicable examples to illustrate the obtained result../files/site1/files/42/4Abstract.pdf
متن کامل