Positive solutions for a system of <em>p</em>-Laplacian boundary value problems


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	Positive solutions for a system of p-Laplacian boundary value problems


	Fixed Point Theory, Volume 19, No. 2, 2018, 823-836, June 1st, 2018 DOI: 10.24193/fpt-ro.2018.2.60 Authors: Jiafa Xu, Donal O'Regan and Keyu Zhang Abstract: In this paper, we investigate the existence of positive solutions for a system of fourth order p-Laplacian boundary value problems $\begin{cases}-((-x''')^{p-1})'=f(t,x,x',y,y'), t\in [0,1],\\ -((-y''')^{p-1})'=g(t,x,x',y,y'), t\in [0,1],\\ x(0)=x'(1)=x''(0)=x'''(1)=0,\\ y(0)=y'(1)=y''(0)=y'''(1)=0, \end{cases}$ where $p>1, f,g\in C([0,1]\times \mathbb{R}^+\times \mathbb{R}^+\times \mathbb{R}^+\times \mathbb{R}^+, \mathbb{R}^+)(\mathbb{R}^+:=[0,\infty))$ . Under some new general conditions on f and g, we use the fixed point index to establish two existence theorems for the above system. The interesting point lies in the fact that the nonlinear term f,g can be allowed to depend on the first derivative of the unknown functions, and this derivative dependence in systems is seldom considered in the literature. Key Words and Phrases: p-Laplacian equation; positive solution; fixed point index; derivative dependence. 2010 Mathematics Subject Classification: 34B18, 47H07, 47H11, 45M20, 26D15. Published on-line: June 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents