Existence of solutions to a superlinear p-Laplacian equation

By Shibo Liu. 2001

74 citations recorded by the source corpus.

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Citations in the corpus

Existence of five nonzero solutions with exact sign for A p-laplacian equation (2009, methodology): “In the best case however, the authors obtain three solutions: a positive, a negative and a nodal solution (see Bartsch-Liu [4], BartschLiu-Weth [5], Carl-Motreanu [9], Zhang-Chen-Li [45], and Zhang-Li [47]).”
Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity (2007, methodology): “In [22] the case λ < λ2 is treated using Morse theory, while [25] deals with the general case, provided that the further condition λ / ∈ σ(− p) is satisfied.”
On superlinear problems without the Ambrosetti and Rabinowitz condition (2010, background): “1 F .x; t / jt j p D C1, where F .x; t / D Z t 0 f .x; s/ds. (1.2) Shibo Liu .f 2 / there exists R > 0 such that for 8x 2 , f .x; t / jt j p2 t is increasing in t R, and decreasing in t Ä R. Note that .f 2 / is a condition for jtj R, therefore it is a quite generic assumption.”
Nontrivial critical groups in $p$-Laplacian problems via the Yang index (2003, unknown): “and the case 1 11 ].”
Existence and multiplicity results for Dirichlet problems with p-Laplacian (2003, methodology): “In [19], the author applied Morse theory to study the case where (f02) and (f∞1) held.”
On ground states of superlinear p-Laplacian equations in RN (2010, background): “On the other hand, the quasilinear case is usually considered on a bounded domain, the reader may find some results in this direction in [4,7,9, 21 ,24].”
Nonlinear Nonhomogeneous Robin Problems with Superlinear Reaction Term (2016, methodology): “Brought to you by | De Gruyter / TCS Authenticated Download Date | 10/24/16 4:53 PM More restrictive versions of hypothesis (Hf ) (iii) were used by Li and Yang [22], Liu [26], Miyagaki and Souto [28], and Sun [38].”
Nontrivial solutions of superlinear p-Laplacian equations (2009, background): “This case was considered in Liu [10], where a nontrivial solution is obtained under the conditions ( f ), ( f0) and (AR).”