On the linearization of some singular, nonlinear elliptic problems and applications

By Jesús A. Hernández, F. J. Mancebo, José Manuel Vega. 2002

92 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2e9e5d2880be073e27dcf8824587ef3da36265da

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Maximum Principles and Principal Eigenvalues (2005, result): “Since the zeros of the function (45) correspond to eigenvalues of (44) having positive eigenfunctions, we can thus extend many of the results for the case 0 (and ), known so far and cited above, to (44) (also see [35], [42] for recent developments).”
Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation (2007, unknown): “(2.10) Inequalities in (2.6) guarantee that B(x) satisfies the conditions of Lemma 2.7 in Hernández, Mancebo, and Vega [30].”
Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, background): “Nonlinear elliptic equation, singularity, boundary blow-up, bifurcation, asymptotic anal- ysis, maximum principle, Karamata regular variation theory.”
On Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Terms (2011, result): “A partial existence result was also found in [17], [16], [18] where, as a particular case of more general results, it was proved directly that the same regularity holds for b > 0 such that a + b < 1, but only for solutions obtained by the method of sub and supersolutions there, and not for any solut”
Lane-Emden-Fowler equations with convection and singular potential (2007, background): “Such singular boundary value problems arise in the context of chemical heterogeneous catalysts and chemical catalyst kinetics, in the theory of heat conduction in electrically conducting materials, singular minimal surfaces, as well as in the study of non-Newtonian fluids or boundary layer phenomena”