Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the -biharmonic

Multiple Solutions for Nonlinear Navier Boundary Systems Involving(p1(x),…,pnMiao1 2016Discrete Dynamics in Nature and Society3010View full textAdd to dashboardCite

“…In recent years, many authors considered the existence and multiplicity of solutions for some fourth order problems [1][2][3][4][5][6][7][8][9][10]. In [4], based on critical point theory, the existence of infinitely many solutions has been established for a class of nonlinear elliptic equations involving the -biharmonic operator and under Navier boundary value conditions.…”

“…In [4], based on critical point theory, the existence of infinitely many solutions has been established for a class of nonlinear elliptic equations involving the -biharmonic operator and under Navier boundary value conditions. The ( )-Laplacian operator is more complicated nonlinearities than -Laplacian; it is inhomogeneous and usually it does not have the so-called first eigenvalue, since the infimum of its principle eigenvalue is zero.…”

Infinitely many solutions for a nonlinear Navier boundary systems involving $(p(x),q(x))$-biharmonic

“…The investigation of existence and multiplicity of solutions for problems involving biharmonic, p-biharmonic and p(x)-biharmonic operators has drawn the attention of many authors, see [2,3,5,6,11] and references therein. Candito and Livrea [5] considered the nonlinear elliptic Navier boundary-value problem ∆(|∆u| p−2 ∆u) = λf (x, u) in Ω,…”

“…Candito and Livrea [5] considered the nonlinear elliptic Navier boundary-value problem ∆(|∆u| p−2 ∆u) = λf (x, u) in Ω,…”

Existence of non-trivial solutions for systems of n fourth order partial differential equations

“…Many authors have studied the existence of at least one solution, or multiple solutions, or even infinitely many solutions for fourth-order boundary value problems by using lower and upper solution methods, Morse theory, the mountain-pass theorem, constrained minimization and concentration-compactness principle, fixed-point theorems and degree theory, and critical point theory and variational methods, and we refer the reader to the papers [2,[4][5][6][7][8][9][10][11] and references therein.…”