混合局部-非局部拟线性问题与混合插值Hardy势
Mixed local-nonlocal quasilinear problems with mixed interpolated Hardy potential
AI总结：
研究一类含混合插值Hardy势的混合局部-非局部拟线性问题，通过建立集中紧性原理并结合Ricceri变分原理和山路定理，得到非线性项在不同增长条件下的解的存在性。
AI中文摘要：
本文研究一类涉及混合插值Hardy势的混合局部-非局部问题非平凡解的存在性。我们首先建立了混合局部和非局部算子的集中紧性原理。将该结果与Ricceri变分原理相结合，得到了非线性项在不同增长条件下拟线性椭圆问题的一个存在性结果。此外，我们应用经典的山路定理，在超线性情形下得到了第二个存在性结果。
英文摘要：
This paper addresses the existence of nontrivial solutions to a class of mixed local-nonlocal problems involving a mixed interpolated Hardy potential. We first establish a concentration-compactness principle for mixed local and nonlocal operators. This result is combined with Ricceri's variational principle to obtain an existence result for quasilinear elliptic problems under different growth assumptions on the nonlinearity. Furthermore, we apply the classical mountain pass theorem to obtain a second existence result in the superlinear case.
