混合分数阶p-Laplace算子方程积分边值问题的多解性

Multiplicity of Solutions for Integrated Boundary Value Problems of Mixed Fractional p-Laplacian Operator Equations

研究了一类同时具有Riemann-Liouville导数和Caputo导数的混合型分数阶p-Laplace算子方程在Riemann-Stieltjes积分边界条件下的正解的存在性。根据Riemann-Stieltjes积分性质,建立了边值问题具有多个正解存在的结论。分别运用不动点定理和单调迭代方法证明了所得结论的正确性,并建立了求解此类边值问题的近似解的迭代序列。最后给出实例用于说明所得结论的适用性。

The existence of positive solutions was studied for a class of mixed fractional p-Laplacian operator equations with both Riemann-Liouville derivatives and Caputo derivatives under RiemannStieltjes integral boundary conditions. According to the Riemann-Stieltjes integral properties, several conclusions were obtained about the existence of multiple positive solutions of boundary value problems by using the fixed point theorem and monotone iterative method. Iterative sequences were established for finding the approximate solutions of such boundary value problems. Finally, some examples were presented to demonstrate the applicability of the conclusions.