Existence results for nonlinear elliptic problems on fractal domains

Abstract

Some existence results for a parametric Dirichlet problem defined on the Sierpi\'nski fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution

Existence of Multiple Solutions of a Kirchhoff Type $p$-Laplacian Equation on the Sierpiński Gasket

“…Under suitable conditions, they have shown the existence of at least two nontrivial weak solutions and one weak solution, respectively to the above problems for a certain range of λ. Many authors have studied different types of equations involving Laplacian on the Sierpiński gasket, we cite a few of them which are related to this article [2,10,12,23]. Now we will discuss about Kirchhoff type equations on regular domains.…”

Nonlinear problems on the Sierpiński gasket

“…In the case when f (·, 0) = 0, in order to get the existence of a non-trivial solution for (1.1) (and so a multiplicity result) we need some extra assumptions on the nonlinear term f . For instance, in [16] the authors assumed the following subquadratical growth condition at zero lim inf 2). Then, applying Theorem 1.1 with λ = 1 we obtain that problem (1.11) admits at least two non-trivial weak solutions one of which lies in B M 2 0 /(2N +3) 2 .…”

On the existence of solutions to a (p,q)‐Laplacian system on the Sierpiński gasket on ℝN−1

“…One can cite, for example, in earlier research. 11,[20][21][22][23][24][25][26][27][28] The reader can also consult 29 for an overview and other references on the subject.…”

“…These definitions allowed an intensive study of elliptic equations on such domains. One can cite, for example, in earlier research 11,20–28 . The reader can also consult 29 for an overview and other references on the subject.…”