scholarly journals Infinitely many solutions for p-harmonic equation with singular term

Author(s):  
Huazhao Xie ◽  
Jianping Wang
Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5003-5010 ◽  
Author(s):  
Chaharlang Makvand ◽  
A. Razani

Here, a fourth order singular elliptic problem involving p-biharmonic operator with Dirichlet boundary condition is established where the exponent in the singular term is different from that in the p-biharmonic operator. The existence of infinitely many solutions is proved by the variational methods in Sobolev spaces and the critical points principle of Ricceri. Finally, an example is presented.


Author(s):  
Yunru Bai ◽  
Nikolaos S. Papageorgiou ◽  
Shengda Zeng

AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$ λ . Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.


2003 ◽  
Vol 17 ◽  
pp. 129-151 ◽  
Author(s):  
Mario Gómez-Torrente

Quotation marks are ambiguous, although the conventional rules that govern their different uses are similar in that they contain quantifications over quotable expressions. Pure uses are governed by a simple rule: by enclosing any expression within quotation marks one gets a singular term, the quotation, that stands for the enclosed expression. Impure uses are far less simple. In a series of uses the quotation marks conventionally indicate that (part of) the enclosed expression is a contextually appropriate version of expressions uttered by some relevant agent. When the quotation marks have this meaning, it is tempting to think of them as contributing that indication to the truth-conditional content of the utterance. I adopt a cautious attitude towards this hypothesis, for the evidence in its favor is inconclusive. In other uses the quotation marks conventionally indicate that the enclosed expression should be used not “plainly” but in some broadly speaking “distanced” way, or that it is being so used by the utterer, and typically context makes clear the exact nature of the “distance” at stake. In these cases the quotation marks do not even appear to contribute that indication to the truth-conditional content of the utterance.


2016 ◽  
Vol 19 (1) ◽  
pp. 815-831 ◽  
Author(s):  
David Arcoya ◽  
Lourdes Moreno-Mérida
Keyword(s):  

2010 ◽  
Vol 2010 (1) ◽  
pp. 584843
Author(s):  
Fu Yongqiang ◽  
Yu Mei

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