论文标题
一类椭圆方程涉及具有签名重量功能的一般非局部非局部集成差异操作员
A class of elliptic equations involving a general nonlocal integrodifferential operators with sign-changing weight functions
论文作者
论文摘要
在本文中，我们调查了一类椭圆方程（$ \ Mathscr {p} $）的非平凡弱解决方案，其中涉及一般的非局部非局部综合差异操作员$ \ MATHSCR {l} _ {\ MATHCAL {\ MATHCAL {a} k} k} $，两个真实的参数，并且可以证明这两个重量函数，以及两个真正的权重函数。考虑到有关该问题所涉及的非线性增长的不同情况（$ \ Mathscr {p} $），我们证明存在两个非平凡的不同解决方案，并且存在一个连续的特征值家族。主要结果的证明是基于使用Nehari方法，Ekelands变异原理和变化计算的直接方法基于基态解决方案。困难源于操作员$ \ Mathscr {l} _ {\ Mathcal {a} k} $不是均匀的，而非线性术语不确定。
In this paper, we investigate the existence of nontrivial weak solutions to a class of elliptic equations ($\mathscr{P}$) involving a general nonlocal integrodifferential operator $\mathscr{L}_{\mathcal{A}K}$, two real parameters, and two weight functions, which can be sign-changing. Considering different situations concerning the growth of the nonlinearities involved in the problem ($\mathscr{P}$), we prove the existence of two nontrivial distinct solutions and the existence of a continuous family of eigenvalues. The proofs of the main results are based on ground state solutions using the Nehari method, Ekelands variational principle, and the direct method of the calculus of variations. The difficulties arise from the fact that the operator $\mathscr{L}_{\mathcal{A}K}$ is nonhomogeneous and the nonlinear term is undefined.
