Existence of Positive Solutions for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function  

作　　者：Alhussein Mohamed Alhussein Mohamed(College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China)

机构地区：[1]College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China

出　　处：《Applied Mathematics》2021年第4期311-321,共11页应用数学（英文）

摘　　要：In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where </span><span style="white-space:nowrap;"><em>f</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span></span> <em>C</em>([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;"><em>α</em></span> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span> </span>[0,6)</span> and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions.In this article, by using a fixed point theorem, we study following fourth-order three-point BVP:<br /> <img src="Edit_1ba3ab24-dbef-4a90-8fe1-dc466461e2e3.bmp" alt="" /> <span style="white-space:normal;">where </span><span style="white-space:nowrap;"><em>f</em> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span></span> <em>C</em>([0,1]×[0,+∞),[0,+∞)) <span style="white-space:nowrap;"><em>α</em></span> <span style="white-space:nowrap;"><span style="white-space:nowrap;">∈</span> </span>[0,6)</span> and <img src="Edit_35fdded4-50be-48af-b9e0-1e97c719aeba.bmp" alt="" /> . The main point to emphasize is that although the corresponding Green’s function is changing signs, by applying the fixed point theorem, we can still obtain at least two positive solutions and degreased solutions under certain suitable conditions.

关 键 词：Fourth-Order Fourth-Point Boundary Value Problem Function Positive Solution EXISTENCE Fixed Point Greens Function 

分 类 号：O17[理学—数学]