In: Mathematica Slovaca, vol. 68, no. 4
Katarzyna Szymańska-Dębowska
Details:
Year, pages: 2018, 837 - 844
Keywords:
nonlocal boundary conditions, resonant problem, nonlinear problem, $p$-Laplacian, coincidence theory
About article:
Our aim is to study the existence of solutions for the following system of nonlocal resonant boundary value problem
$$ (φ (x'))' =f(t,x,x'), x'(0)=0, x(1)=\int01x(s)\dd g(s), $$
where the function $\f :\Rn\to\Rn$ is given by $\f (s)=(\Fp1(s1), … ,\Fpn(sn))$, $s\in\Rn$, $pi >1$ and $\Fpi:\R\to\R$ is the one dimensional $pi$-Laplacian, $i=1,… ,n$, $f:[0,1]×\mathbb{R}n× \mathbb{R}n\to\mathbb{R}n$ is continuous and $g:[0,1]\to\mathbb{R}n$ is a function of bounded variation. The proof of the main result is depend upon the coincidence degree theory.How to cite:
ISO 690:
Szymańska-Dębowska, K. 2018. System of nonlocal resonant boundary value problems involving $p$-Laplacian. In Mathematica Slovaca, vol. 68, no.4, pp. 837-844. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0149
APA:
Szymańska-Dębowska, K. (2018). System of nonlocal resonant boundary value problems involving $p$-Laplacian. Mathematica Slovaca, 68(4), 837-844. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0149
About edition:
Published: 10. 8. 2018