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On the existence of three solutions for quasilinear elliptic problem

Goncerz P.

Opuscula Mathematica

2012

Vol. 32, no. 3

473-486

We consider a quasilinear elliptic problem of the type - Δpu = λ (ƒ (u)+ μg(u)) in Ω, u/∂Ω = 0, where Ω ⊂ RN is an open and bounded set, ƒ, g are continuous real functions on R and , λ, μ ∈ R. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.

Comparison of two types of Trefftz method for the solution of inhomogeneous elliptic problems

Uściłowska-Gajda A., Kołodziej J. A., Ciałkowski M., Frąckowiak A.

Computer Assisted Mechanics and Engineering Sciences

2003

Vol. 10, No. 4

661-675

The solution of inhomogeneous elliptic problems by the Trefftz method has become increasingly more popular during the last decade. One method of solution uses the fundamental solutions as trial functions and the inhomogeneous part is expressed by radial basis functions (RBFs). The purpose of this paper is to solve several boundary value problems that have exact solutions. Two error criteria are used for comparison of the exact solutions and the approximated solutions. The first is the mean least square global error. The second has a local character, as it measures the absolute maximal error.