Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems

By Zhijun Zhang, Jian Cheng. 2004

100 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/22ba4859afadd638dd619ca2d6d281034b1b42d3

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Terms (2011, background): “(This result was extended later by Zhang and Cheng [23] for h(x) = d(x)β , with β > 0, where d(x) = dist(x, ∂Ω)).”
Finite and infinite energy solutions of singular elliptic problems: Existence and uniqueness (2016, background): “1), also called sing ular Lane–Emden–Fowler equations, has been also extended to the case in which the term s−γ is replaced by aC1 nonincreasing nonlinearity h(s) that blows up at zero at a given rate (see [43, 15, 33, 48]).”
Positive solutions of the p-Laplace equation with singular nonlinearity (2009, methodology): “5 is proved in [34] for the case p = 2 under a different set of assumptions on b and g.”
Combined effects in mixed local–nonlocal stationary problems (2021, background): “For similar works concerning the local elliptic or integral equations with purely singular nonlinearities, we refer to [51, 30, 33, 47, 18] and singular 4”
Semilinear elliptic equations with singular nonlinearities (2010, background): “The results of Lazer and McKenna were then generalized by Lair and Shaker (see [12 ]a nd [13], where the function g is of the form f (x) g(u)), and by Zhang and Cheng (see [ 18 ], where the function g is of the form f (x) g(u) and f may not even be in L 1 (�) ). In all these papers a major role is p”
The asymptotic behaviour of the unique solution for the singular Lane–Emden–Fowler equation (2005, background): “The problem was discussed and extended to the more general problems in number of works; see, for instance, [2,9–17,19–21,23,28–33].”
Lane-Emden-Fowler equations with convection and singular potential (2007, result): “Our results in this case generalize those established in [32], in the sense that in the present paper we do not prescribe the behavior of the singular nonlinearity g around the origin.”
Boundary Value Problems for Singular Elliptic Equations (2011, result): “Lair and Shaker [9] and Zhang and Cheng [21] have obtained the results of Lazer and McKenna (in the case 0 γ 1) deducing the existence of solutions of   is either a bounded domain or the whole space R N , (while Ω in [21] is bounded) and the conditions on a in [9] are weaker than those in…”
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases (2011, background): “Problems of this kind are discussed in many papers; see, for instance, [5, 6, 8, 9, 11, 12] and references therein.”