BOUNDARY VALUE PROBLEM INVOLVING THE p-LAPLACIAN ON THE SIERPIŃSKI GASKET

Fractals ◽  
2018 ◽  
Vol 26 (01) ◽  
pp. 1850007 ◽  
Author(s):  
AMIT PRIYADARSHI ◽  
ABHILASH SAHU
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Sierpinski Gasket ◽  
Sierpiński Gasket

In this paper, we study the following boundary value problem involving the weak [Formula: see text]-Laplacian. [Formula: see text] [Formula: see text] where [Formula: see text] is the Sierpiński gasket in [Formula: see text], [Formula: see text] is its boundary, [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are bounded nonnegative functions. We will show the existence of at least two nontrivial weak solutions to the above problem for a certain range of [Formula: see text] using the analysis of fibering maps on suitable subsets.

EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 61 (3) ◽  
pp. 305-319
Author(s):  
CRISTIAN-PAUL DANET
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

scholarly journals Entropy Solution for Doubly Nonlinear Elliptic Anisotropic Problems with Robin Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
I. Ibrango ◽  
S. Ouaro
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Boundary Value ◽  
Monotone Operators ◽  
Robin Boundary Conditions ◽  
Anisotropic Problems ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

We study in this paper nonlinear anisotropic problems with Robin boundary conditions. We prove, by using the technic of monotone operators in Banach spaces, the existence of a sequence of weak solutions of approximation problems associated with the anisotropic Robin boundary value problem. For the existence and uniqueness of entropy solutions, we prove that the sequence of weak solutions converges to a measurable function which is the entropy solution of the anisotropic Robin boundary value problem.

scholarly journals Boundary value problem: Weak solutions induced by fuzzy partitions

2020 ◽  
Vol 25 (2) ◽  
pp. 715-732 ◽  
Author(s):  
Linh Nguyen ◽  
◽  
Irina Perfilieva ◽  
Michal Holčapek
Keyword(s):  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Fuzzy Partitions

Existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem

2019 ◽  
Vol 61 ◽  
pp. 305-319
Author(s):  
Cristian Paul Danet
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles. doi:10.1017/S1446181119000129

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