SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS

By J. G. Azorero, I. P. Alonso, Juan J. Manfredi. 2000

354 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5d90aff7c41c3bb4e8080843db0003f72440a6f2

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Anisotropic nonlinear Neumann problems (2011, methodology): “For constant exponent Dirichlet Sobolev spaces, the result was obtained by Brezis–Nirenberg [7] (for p = 2), García Azorero–Manfredi–Peral Alonso [21] (for p > 1) and Guo–Zhang [25] (for p 2).”
On the connection between two quasilinear elliptic problems with source terms of order 0 or 1 (2008, background): “It has been obtained for power-type nonlinearities of type concave-convex, see [6], [34], and [2] for general convex function g and p = 2, and some results are given in [28] for a power and p > 1.”
Existence of multiple solutions with precise sign information for superlinear Neumann problems (2009, background): “[17] (see also Guo and Zhang [20], and for a nonsmooth version, Kyritsi and Papageorgiou [21]).”
Multiple solutions with precise sign for nonlinear parametric Robin problems (2014, background): “[11] J.P. Garcia Azorero, J. Manfredi, I. Peral Alonso, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations, Commun.”
Coercive and noncoercive nonlinear Neumann problems with indefinite potential (2016, background): “5 was first proved for the Dirichlet Sobolev space H1 0 (Ω) and for G(y) = (1)2 ‖y‖2 (y ∈ RN) by Brezis and Nirenberg [6] and it was extended to the Dirichlet Sobolev space W1,p 0 (Ω) (1 < p < ∞) and for G(y) = 1 p ‖y‖p (y ∈ RN) by Garcia Azorero, Manfredi and Peral Alonso [14].”
Local minimizers over the Nehari manifold for a class of concave-convex problems with sign changing nonlinearity (2017, methodology): “Finally, the result was generalized for p > 1 by Azorero-Peral-Manfredi in [3].”
Existence of five nonzero solutions with exact sign for A p-laplacian equation (2009, methodology): “In [25], Z ⊂ R is an arbitrary bounded domain with a smooth boundary and the approach is variational.”
A multiplicity results for a singular equation involving the p(x)-Laplace operator (2017, methodology): “Using constraints based on Lp- norms rather than Sobolev norms as in [25], the equations for which uniform estimates are required can be simplified to a standard type involving only one p-Laplace operator.”
Local "superlinearity"and "sublinearity" for the p-Laplacian (2009, background): “in [12],[18].”
Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian (2008, methodology): “In [11], Z ⊆ R is an arbitrary bounded domain with a smooth boundary and their approach is variational based on the critical point theory.”