The Existence of Multiple Solutions to Quasilinear Elliptic Equations

By Jiaquan Liu, Shibo Liu. 2005

51 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e4e72d5cbdbcb507d0f355d20723a383befec2a5

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Multiple solutions for coercive p-Laplacian equations (2006, background): “for p = 2 and [ 12 ] for general p> 1. Obviously, this ‘superlinear’ condition is stronger than (f 2 0 ).”
Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian (2008, background): “9 improves the multiplicity results of [17] and [18].”
Anisotropic nonlinear Neumann problems (2011, unknown): “We mention the works of Bartsch–Liu [6], Carl–Perera [8], Dancer–Perera [12], Filippakis–Kristaly– Papageorgiou [20], Gasiński–Papageorgiou [23], Liu–Liu [30], Papageorgiou–Papageorgiou [34,35] and Zhang–Chen–Li [38].”
Morse Theoretic Aspects of $p$-Laplacian Type Operators (2010, background): “[72] Jia Quan Liu and Shu Jie Li.”
Coercive and noncoercive nonlinear Neumann problems with indefinite potential (2016, methodology): “Three solutions theorems for coercive nonlinear equations driven by the p-Laplacian (that is, we have a(y) = ‖y‖p−2y for all y ∈ RN, 1 < p < ∞) were proved by Liu [25], Liu and Liu [24] and Kyritsi and Papageorgiou [21].”
Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator (2011, background): “Recently, such multiplicity results were proved for the coercive Dirichlet problem driven by the p-Laplacian in [4, 12, 13, 16, 17, 20, 23] (see also [5, 9] for slightly more general differential operators producing two constant sign solutions).”
Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential (2012, methodology): “Remark 4.5 Compared with the results of Liu-Liu [27, Theorem 1.1] and Liu [28, Theorem 1.2], our work here is more general in many respects.”
Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance (2014, methodology): “To do this we do not need the stronger conditions on f (z, ·) and in the proof we use some ideas of Liu [31].”