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Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

Gabriele Bonanno, Giovanni Molica Bisci, Vicenţiu Rădulescu (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.

Variational methods for a resonant problem with the $p$ -Laplacian in $ℝ^{N}$ .

Alziary, Benedicte, Fleckinger, Jacqueline, Takáč, Peter (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Very weak solutions of the stationary Stokes equations in unbounded domains of half space type

Reinhard Farwig, Jonas Sauer (2015)

Mathematica Bohemica

We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as $ℝ_{+}^{n}$ , bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of $ℝ_{+}^{n}$ , and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous...

Displaying 1 – 3 of 3

Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

Variational methods for a resonant problem with the p -Laplacian in ℝ N .

Very weak solutions of the stationary Stokes equations in unbounded domains of half space type

Currently displaying 1 – 3 of 3

Variational methods for a resonant problem with the $p$ -Laplacian in $ℝ^{N}$ .