scholarly journals Existence of Infinitely Many High Energy Solutions for a Fourth-Order Kirchhoff Type Elliptic Equation in R<sup>3</sup>

2020 ◽  
Vol 08 (08) ◽  
pp. 1550-1559
Author(s):  
Ting Xiao ◽  
Canlin Gan ◽  
Qiongfen Zhang
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yuanfang Ru ◽  
Fanglei Wang ◽  
Yunhai Wang ◽  
Tianqing An

We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian Δ2u-a+b∫Ω∇u2dxΔu=fx,u,∇u,Δu, in Ω, u=0, Δu=0, on ∂Ω, where a, b are positive constants. We will show that there exists b⁎>0 such that the problem has a nontrivial solution for 0<b<b⁎ through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.


GeoArabia ◽  
2003 ◽  
Vol 8 (1) ◽  
pp. 47-86 ◽  
Author(s):  
Jürgen Grötsch ◽  
Omar Suwaina ◽  
Ghiath Ajlani ◽  
Ahmed Taher ◽  
Reyad El-Khassawneh ◽  
...  

ABSTRACT A 3-D geological model of the Kimmeridgian-Tithonian Manifa, Hith, Arab, and Upper Diyab formations in the area of the onshore Central Abu Dhabi Ridge was based on a newly established sequence stratigraphic, sedimentologic, and diagenetic model. It was part of an inter-disciplinary study of the large sour-gas reserves in Abu Dhabi that are mainly hosted by the Arab Formation. The model was used for dynamic evaluations and recommendations for further appraisal and development planning in the studied field. Fourth-order aggradational and progradational cycles are composed of small-scale fifth-order shallowing-upward cycles, mostly capped by anhydrite within the Arab-ABC. The study area is characterized by a shoreline progradation of the Arab Formation toward the east-northeast marked by high-energy oolitic/bioclastic grainstones of the Upper Arab-D and the Asab Oolite. The Arab-ABC, Hith, and Manifa pinch out toward the northeast. The strongly bioturbated Lower Arab-D is an intrashelf basinal carbonate ramp deposit, largely time-equivalent to the Arab-ABC. The deposition of the Manifa Formation over the Arab Formation was a major back-stepping event of the shallow-water platform before the onset of renewed progradation in the Early Cretaceous. Well productivity in the Arab-ABC is controlled mainly by thin, permeable dolomitic streaks in the fifth-order cycles at the base of the fourth-order cycles. This has major implications for reservoir management, well completion and stimulation, and development planning. Good reservoir properties have been preserved in the early diagenetic dolomitic streaks. In contrast, the reservoir properties of the Upper Arab-D oolitic/bioclastic grainstones deteriorate with depth due to burial diagenesis. A rock-type scheme was established because complex diagenetic overprinting prevented the depositional facies from being directly related to petrophysical properties. Special core analysis and the attribution of saturation functions to static and dynamic models were made on a cell-by-cell basis using the scheme and honoring the 3-D depositional facies and property model. The results demonstrated the importance of integrating sedimentological analysis and diagenesis with rock typing and static and dynamic modeling so as to enhance the predictive capabilities of subsurface models.


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