我們研究一維空間p-拉普拉斯多參數擴散問題
(φ_{p}(u'(x)))' + λ(ku^{p-1} + ∑_{i=1}^{m} a_{i} u^{q_{i}}) - μ∑_{j=1}^{n} b_{j} u^{r_{j}} = 0, -1 < x < 1, u(-1) = u(1) = 0, 其中p > 1，(φ_{p}(u'(x)))' 是一維p-拉普拉斯算子, 且 λ > 0，μ ≥ 0 是兩個分枝參數。我們假設 k ≥ 0, 0 < p-1 < q_{1} < q_{2} < ⋅⋅⋅ < q_{m} < r_{1} < r_{2} < ⋅⋅⋅ <r_{n}, m,n ≥ 1, a_{1}= 1, a_{i} > 0 當 i=1,2,…,m 且b_{1}=1, b_{j} > 0 當j=1,2,…,n. 我們主要證明，在(λ,||u||_{∞})-平面，分枝圖由嚴格遞減曲線組成當μ=0，並且始終由⊂形曲線組成當 μ > 0。然後，我們研究了當 μ ≥ 0變化時分枝圖的結構和演化。

We study the multiparameter p-Laplacian Dirichlet problem
(φ_{p}(u'(x)))' + λ(ku^{p-1} + ∑_{i=1}^{m} a_{i} u^{q_{i}}) - μ∑_{j=1}^{n} b_{j} u^{r_{j}} = 0, -1 < x < 1, u(-1) = u(1) = 0,
where p > 1, φ_{p}(y) = |y|^{p-2} y, (φ_{p}(u'(x)))' is the one-dimensional p-Laplacian, λ > 0 and μ ≥ 0 are two bifurcation parameters. We assume that k ≥ 0, 0 < p-1 < q_{1} < q_{2} < ⋅⋅⋅ < q_{m} < r_{1} < r_{2} < ⋅⋅⋅ <r_{n}, m,n ≥ 1, a_{1}= 1, a_{i} > 0 for i=1,2,...,m and b_{1}=1, b_{j} > 0 for j = 1, 2, ..., n. We mainly prove that, on the (λ,||u||_{∞})-plane, the bifurcation diagram consists of a strictly decreasing curve for μ = 0, and always consists of a ⊂-shaped curve for fixed μ > 0. We then study the structures and evolution of the bifurcation diagrams with varying μ ≥ 0.

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