scholarly journals Adaptive fixed point iterations for semilinear elliptic partial differential equations

CALCOLO ◽  
2019 ◽  
Vol 56 (3) ◽  
Author(s):  
Mario Amrein
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Semilinear Elliptic ◽  
Fixed Point Iterations

scholarly journals Existence of Positive Solution for a Nonlinear Weighted Bi-Harmonic System of Elliptic Partial Differential Equations via Fixed-Point Argument

2020 ◽  
Vol 40 (1) ◽  
pp. 54-70
Author(s):  
Md Asaduzzamana ◽  
Md Zulfikar Ali
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Positive Solution ◽  
A Priori ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Existence Criterion ◽  
Point Argument ◽  
Harmonic System

In this paper, we establish an existence criterion of positive solution for a nonlinear weighted bi-harmonic system of elliptic partial differential equations in the unit ball in Nn ( dimensionaleuclideanspace) The analysis of this paper is based on a topological method (a fixed-point argument). Initially, we establish a priori solution estimates, and then use a fixed-point theorem for deducing the existence of positive solutions. Finally, we prove a non-existence criterion as the complement of existence criterion. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 54-70

scholarly journals Some maximum principles for solutions of a class of partial differential equations inΩ⊂ℝn

2000 ◽  
Vol 24 (11) ◽  
pp. 749-751
Author(s):  
Mohammad Mujalli Al-Mahameed
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Partial Differential Equations ◽  
Maximum Principles ◽  
Partial Differential ◽  
Semilinear Elliptic

We find maximum principles for solutions of semilinear elliptic partial differential equations of the forms: (1)Δ2u+αf(u)=0,α∈ℝ+and (2)ΔΔu+α(Δu)k+gu=0,α≤0in some regionΩ⊂ℝn.

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