Existence of nontrivial solution for quasilinear equations involving the 1-biharmonic operator

Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Higher-order elliptic equations (35J30)

Cites Work

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Limiting Sobolev inequalities and the 1-biharmonic operator
On Palais' principle for non-smooth functionals
Anisotropic \(p,q\)-Laplacian equations when \(p\) goes to 1
Nonlinear scalar field equations. I: Existence of a ground state
Higher-order functional inequalities related to the clamped 1-biharmonic operator
The concentration-compactness principle in the calculus of variations. The locally compact case. II
On the solutions to 1-Laplacian equation with \(L^1\) data
Variational methods for non-differentiable functionals and their applications to partial differential equations
Parabolic quasilinear equations minimizing linear growth functionals
Strauss' and Lions' type results in \(BV(\mathbb R^N)\) with an application to an 1-Laplacian problem
On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator
Nehari method for locally Lipschitz functionals with examples in problems in the space of bounded variation functions
Some existence results of bounded variation solutions to 1-biharmonic problems
Minimizing total variation flow
A Berestycki-Lions' type result to a quasilinear elliptic problem involving the 1-Laplacian operator
Functions of least gradient and 1-harmonic functions
The Euler Equation for Functionals with Linear Growth
The Dirichlet problem for a singular elliptic equation arising in the level set formulation of the inverse mean curvature flow
The eigenvalue problem for the 1-biharmonic operator
On a quasilinear elliptic problem involving the 1-biharmonic operator and a Strauss type compactness result

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