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For a long time, the characteristics and main controlling factors of the sweet spot reservoir of tight sandstone gas in the first member of the Shihezi Formation in Hangjinqi area of Ordos Basin are not clear, which restricts the natural gas productivity in this area.Core observations, rock slice image, mercury intrusion experiments and logging data, etc.are used comprehensively to determine the petrological characteristics, reservoir physical properties, sedimentary facies and diagenesis of the tight and high-yield reservoir in the first member of the Lower Shihezi Formation in well J58 block of the Hangjinqi area, Ordos Basin.In-depth research was carried out to identify and classify the favorable sedimentary-diagenetic facies types of the first member of the Lower Shihezi Formation in the study area to establish the corresponding relationship between logging response characteristics and sedimentary diagenetic facies, and discuss the development law and main controlling factors of sedimentary microfacies controlled sweet spots in well J58 block.The results show that there are still many sweet spots in the reservoir of Hangjinqi area under the condition of compact rock formation.The lithology of high gas producing area is mainly litharenite and lithic quartzite, with large particles and good sorting.The original sedimentary environment is mainly braided stream delta with strong hydrodynamic force.Besides, dessert area is mainly controlled by sedimentary facies, and it is mainly developed in high-energy sedimentary facies and favorable diagenesis facies.The prediction and evaluation of dessert reservoir focus on the medium weak compaction debris dissolution diagenetic facies and high-energy beach sedimentary microfacies.

In this paper, we consider the following quasilinear Schrödinger equation: −Δu+V(x)u+κ2Δ(u2)u=K(x)f(u),x∈RN,-\Delta u+V\left(x)u+\frac{\kappa }{2}\Delta \left({u}^{2})u=K\left(x)f\left(u),\hspace{1.0em}x\in {{\mathbb{R}}}^{N}, where N≥3N\ge 3, κ>0\kappa \gt 0, f∈C(R,R)f\in {\mathcal{C}}\left({\mathbb{R}},{\mathbb{R}}), V(x)V\left(x) and K(x)K\left(x) are positive continuous potentials. Under given conditions, by changing variables and truncation argument, the energy of ground state solutions of the Nehari type is achieved. We also prove the existence of ground state sign-changing solutions for the aforementioned equation. Our results are the generalization work of M. B. Yang, C. A. Santos, and J. Z. Zhou, Least action nodal solution for a quasilinear defocusing Schrödinger equation with supercritical nonlinearity, Commun. Contemp. Math. 21 (2019), no. 5, 1850026, https://doi.org/10.1142/S0219199718500268.

In this paper, we study the following generalized Kadomtsev-Petviashvili equation ut+uxxx+(h(u))x=Dx−1Δyu,{u}_{t}+{u}_{xxx}+{\left(h\left(u))}_{x}={D}_{x}^{-1}{\Delta }_{y}u, where (t,x,y)∈R+×R×RN−1\left(t,x,y)\in {{\mathbb{R}}}^{+}\times {\mathbb{R}}\times {{\mathbb{R}}}^{N-1}, N≥2N\ge 2, Dx−1f(x,y)=∫−∞xf(s,y)ds{D}_{x}^{-1}f\left(x,y)={\int }_{-\infty }^{x}f\left(s,y){\rm{d}}s, ft=∂f∂t{f}_{t}=\frac{\partial f}{\partial t}, fx=∂f∂x{f}_{x}=\frac{\partial f}{\partial x} and Δy=∑i=1N−1∂2∂yi2{\Delta }_{y}={\sum }_{i=1}^{N-1}\frac{{\partial }^{2}}{{\partial }_{{y}_{i}}^{2}}. We get the existence of infinitely many nontrivial solutions under certain assumptions in bounded domain without Ambrosetti-Rabinowitz condition. Moreover, by using the method developed by Jeanjean [13], we establish the existence of ground state solutions in RN{{\mathbb{R}}}^{N}.

Abstract Based on previous notions of expansive mapping, times reasonable expansive mapping is defined. The existence of fixed point for times reasonable expansive mapping is discussed and some new results are obtained.

In this paper, we study the following Schrödinger–Kirchhoff type equation: (a + b ∬ R 2 N | u (x) − u (y) | p | x − y | N + p s d x d y) (− Δ) p s u + λ V (x) | u | p − 2 u = h (x) | u | r − 2 u + g (x) | u | q − 2 u , x ∈ R N , where s ∈ (0 , 1) , 2 ≤ p < ∞ , N>ps, 1 < q < p < r < p s ∗ and a , λ > 0 , b ≥ 0 are three real parameters. By using the mountain pass theorem and a variant version of Ekeland's variational principle in Zhong [A generalization of Ekeland's variational principle and application to the study of relation between the weak P.S. condition and coercivity. Nonlinear Anal. 1997;29:1421–1431], we get some results. Firstly, we obtain a positive energy solution u b , λ + by a truncated functional and discuss their asymptotical behavior for λ → + ∞ when p0, we obtain a positive energy solution u λ + and discuss their asymptotical behavior for λ → + ∞ when 2 p ≤ r < p s ∗ , where p s ∗ = N p N − s p . Moreover, we obtain other asymptotical behavior of positive energy solution when p < r < p s ∗ . Finally, we get a negative energy solution and the non-existence of the non-trivial solutions. [ABSTRACT FROM AUTHOR]

Honghe oilfield is located in the southern Tianhuan Depression of the Ordos Basin. The Upper Triassic Yanchang Formation is in a normal or negative pressure state. The reservoir is tight with low permeability. The time relationship between reservoir densification and formation is very important in the dynamic mechanism analysis of hydrocarbon accumulation in tight sandstones. Combined with microfacies analysis of fluid inclusions, isotopic chronology of authigenic illite, numerical simulation of hydrocarbon generation evolution, and observation statistics under a microscope, this relationship is studied in the Yanchang Formation, and the reservoir forming mechanism of a tight sandstone under low dynamic background is analyzed. The results show that diagenesis and oil accumulation of the Yanchang Formation in the Honghe oilfield occur synergistically, and large-scale reservoir formation is earlier than the key densification event. The Yanchang Formation reservoir is the result of early filling, dominant channel, differential pressure driving, and other mechanisms under a low dynamic background, which shows the characteristics of early selective filling, late inherited filling, and disseminated expansion. The coupling evolution relationship between reservoir forming dynamics and resistance of different sandstones determines the differential accumulation and enrichment of strongly heterogeneous reservoirs. [ABSTRACT FROM AUTHOR]