Abstract Using elements of the theory of linear operators in Hilbert spaces and monotonicity tools we obtain the existence and uniqueness results for a wide class of nonlinear problems driven by the equation T x = N ( x ) Tx=N\left(x) , where T T is a self-adjoint operator in a real Hilbert space ℋ {\mathcal{ {\mathcal H} }} and N N is a nonlinear perturbation. Both potential and nonpotential perturbations are considered. This approach is an extension of the results known for elliptic operators.

中文翻译：

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自伴算子的非线性扰动

其中 TT 是真实希尔伯特空间 ℋ {\mathcal{ {\mathcal H} }} 中的自伴算子，NN 是非线性扰动。潜在的和非潜在的扰动都被考虑在内。这种方法是椭圆算子已知结果的扩展。