INFINITELY MANY SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPINSKI GASKET

DOI10.1142/S0219530511001844zbMath1229.35049OpenAlexW2115631688MaRDI QIDQ3173105

Brigitte E. Breckner, Csaba Varga, Vicenţiu D. Rădulescu

Publication date: 10 October 2011

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530511001844

zbMATH Keywords

weak solutionsattractorHausdorff measurenonlinear elliptic equationsSierpinski gasketweak Laplace operator

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Variational methods involving nonlinear operators (47J30) Boundary value problems for second-order elliptic equations (35J25) Nonlinear elliptic equations (35J60) Fractals (28A80) Weak solutions to PDEs (35D30)

Related Items (24)

TWO NONTRIVIAL WEAK SOLUTIONS FOR THE DIRICHLET PROBLEM ON THE SIERPIŃSKI GASKET ⋮ Nonlinear problems on the Sierpiński gasket ⋮ Qualitative analysis of gradient-type systems with oscillatory nonlinearities on the Sierpiński gasket ⋮ Weak solutions for a ( p ,  q )-Laplacian systems with two parameters on PCF-fractal domain ⋮ Existence of a weak solution for a class of nonlinear elliptic equations on the Sierpiński gasket ⋮ On the existence of solutions to a (p,q)‐Laplacian system on the Sierpiński gasket on ℝ^N−1 ⋮ Monotone operators and a class of nonlinear elliptic equations on the Sierpiński gasket ⋮ Existence of multiple solutions of a Kirchhoff type \(p\)-Laplacian equation on the Sierpiński gasket ⋮ On the Application of Monotonicity Methods to the Boundary Value Problems on the Sierpinski Gasket ⋮ MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET ⋮ A note on gradient-type systems on fractals ⋮ Variational treatment of nonlinear equations on the Sierpiński gasket ⋮ One-parameter Dirichlet problems on the Sierpinski gasket ⋮ A class of semilinear elliptic equations on the Sierpinski gasket ⋮ On the mountain pass solutions to boundary value problems on the Sierpinski gasket ⋮ On the existence of three solutions for the Dirichlet problem on the Sierpiński gasket ⋮ Saddle-point solutions to Dirichlet problems on the Sierpiński gasket ⋮ Infinitely many solutions for a class of nonlinear elliptic problems on fractals ⋮ A characterization for elliptic problems on fractal sets ⋮ On Uniqueness of Solutions to the Boundary Value Problems on the Sierpiński Gasket ⋮ Unnamed Item ⋮ Critical point approaches to Gradient-Type systems on the Sierpiński Gasket ⋮ DIRICHLET PROBLEM OF POISSON EQUATIONS ON A TYPE OF HIGHER-DIMENSIONAL FRACTAL SETS ⋮ Multiple solutions of Dirichlet problems on the Sierpinski gasket

Cites Work

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• Solvability for differential equations on fractals
• Semilinear elliptic equations on fractal sets
• Every superposition operator mapping one Sobolev space into another is continuous
• On the multiplicity of the solutions of the equation \(-\Delta u=\lambda \cdot f(u)\)
• Harmonization and homogenization on fractals
• Semilinear PDEs on self-similar fractals
• Nonlinear elliptical equations on the Sierpiński gasket
• Multiple solutions for a class of nonlinear elliptic equations on the Sierpiński gasket
• Localized Eigenfunctions of the Laplacian on p.c.f. Self-Similar Sets
• Partial differential equations on products of Sierpinski gaskets
• Nonsmooth Neumann-Type Problems Involving thep-Laplacian

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