Existence for elliptic equations in having lower order terms with natural growth.

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Existence and nonexistence of solutions for singular quadratic quasilinear equations (2009, methodology): “Here we adapt to our case a technique to obtain the strong convergence of truncations first introduced in [26] (see also [35]).”
Nonlinear equations with natural growth terms and measure data (2002, background): “with 7! H(x,s, ) growing at most like | |p (the so-called natural growth), always admits a solution if f 2 L1() (see [ 42 ]).”
Dirichlet problems with singular and gradient quadratic lower order terms (2008, background): “Puel and to • [4,21]: unbounded solutions and data in the dual space (with the assumption g(x, s, ξ) s ≥ 0); • [9,10,17,27,29]: unbounded solutions and f ∈ L(1)(Ω) (with the assumption (1.”