Existence results for a class of nonlinear elliptic problems with p-growth in the gradient

By N. Grenon, Cristina Trombetti. 2003

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Some remarks on elliptic problems with critical growth in the gradient (2006, background): “Later on, many authors have been considering elliptic equations with first order terms having quadratic growth with respect to the gradients (see for instance [14], [15], [16], [17], [18], [19], [21], [22], [25], [26], [29], [32], [31], [40], [42], [43], [46], [50] and references therein).”
Nonlinear elliptic equations having a gradient term with natural growth (2006, background): “The classical references are [18] and [22]; since then, many authors have proved results for second order elliptic problems with lower order terms depending on the gradient: these works include, for instance, [4], [5], [6], [8], [13], [14], [15], [16], [20], [25], [27], or [29].”
Singular quasilinear equations with quadratic growth in the gradient without sign condition (2009, unknown): “However, a smallness condition on the function a(x) is imposed in [13,16], while in [11,19] the authors consider a general term a(x) but they impose an asymptotic condition on g(x, s).”
Morrey global bounds and quasilinear Riccati type equations below the natural exponent (2014, background): “2) in the natural growth case q = p, see for example [1, 4, 5, 12, 13, 16, 28, 29, 35, 36, 43, 44, 45, 49, 57].”