Bifurcation-type results for nonlinear parametric elliptic equations
Bifurcation-type results for nonlinear parametric elliptic equations
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DOI：
10.1017/s0308210511000126
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发表时间：
2012-06
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影响因子：
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通讯作者：
Leszek Gasińki;Nikolaos S. Papageorgiou
中科院分区：
文献类型：
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作者：
Leszek Gasińki;Nikolaos S. Papageorgiou
考虑一类由p-Laplacian算子驱动的非线性椭圆型方程，其Carathéodory反应依赖于参数λ > 0，寻找正解.我们证明了两个分支型结果。在第一个分支发生在0附近（λ > 0的小值），我们的设置包含了凹和凸非线性的组合效应的问题。在第二种情况下，分支发生在+∞附近（对于λ > 0的大值），我们的设置作为一个特殊情况包含p-logistic方程与超扩散反应。我们的方法是变分的，基于极大极小方法和截断技术。
We consider the nonlinear elliptic equation driven by the p-Laplacian and with a Carathéodory reaction depending on a parameter λ > 0, looking for positive solutions. We prove two bifurcation-type results. In the first the bifurcation occurs near 0 (for small values of λ > 0) and our setting incorporates problems with the combined effects of concave and convex nonlinearities. In the second, the bifurcation occurs near +∞ (for large values of λ > 0) and our setting incorporates as a special case p-logistic equations with superdiffusive reaction. Our approach is variational, based on minimax methods and truncation techniques.