Using numerical methods, we will show the existence of multiple solutions for the equation −∆u = λf (u) with Dirichlet boundary condition in a bounded domain Ω, where λ > 0 and f (u) is a superlinear function of u.
In this work we present a numerical approach for finding positive solutions for −∆u = λ(u + u 2 + u 3) for x ∈ Ω with Dirichlet boundary condition. We will show that in which range of λ, this problem achieves a numerical solution and what is the behavior of the branch of this solutions.
Combination of fly ash (FA) and micro aluminum powder (AL) is an alternative to produce cement composites out of Equisetum (Eq. telmateia) fibers which would have acceptable thermal and mechanical properties. In this study, Type II Portland cement, class F FA, AL, Equisetum telmateia fibers and silica fume gel used to manufacture structural composite boards… (More)
Using a variational approach, we investigate the existence of a nontrivial weak solution for a class of general capillarity systems in R N. The proofs rely essentially on the mountain pass theorm with a weak version of the Palais-Smale conditions, due to Cerami.
Using a numerical method based on sub-super solution, we will obtain positive solution to the coupled-system of boundary value problems of the form −∆u = λ 1 f (v) + µ 1 h(u) in Ω −∆v = λ 2 g(u) + µ 2 γ(v) in Ω u = 0 = v on ∂Ω where −∆ is the Laplacian operator λ 1 , λ 2 , µ 1 , µ 2 are nonnegative parameters, and Ω is a bounded region in R n , with smooth… (More)