含Φ-Laplace算子和奇异非线性项的拟线性椭圆型方程正解的分歧性
Bifurcation of Positive Solutions for Quasilinear Elliptic Equations with Φ-Laplacian Operator and Singular Nonlinearity
摘要: 本文研究了一类具有Φ-Laplace算子和奇异非线性项的拟线性椭圆型方程正解的存在性及相关问题。利用临界点理论、截断技巧和比较原理，证明了解的分歧性；进一步得到了最小正解的存在性及其关于参数λ的单调性和连续性。
Abstract: In this paper, we study the existence of positive solutions and related problems for a class of quasilinear elliptic equations with Φ-Laplacian operator and singular nonlinearity. We obtain the bifurcation of solutions by using critical point theory, appropriate truncation and comparison techniques. Furthermore, we obtain the existence of the smallest positive solution and the monotonicity and continuity with respect to parameter λ.
文章引用：马金鸽. 含Φ-Laplace算子和奇异非线性项的拟线性椭圆型方程正解的分歧性[J]. 应用数学进展, 2022, 11(4): 2080-2094. https://doi.org/10.12677/AAM.2022.114226

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