System of nonlocal resonant boundary value problems involving $p$-Laplacian

Rok, strany: 2018, 837 - 844

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 $\f (s)=(\F_p1(s₁), … ,\F_pn(s_n))$, $s\in\Rn$, $p_i >1$ and $\F_pi:\R\to\R$ is the one dimensional $p_i$-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.

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