[PDF] Top 20 Solvability for some boundary value problems with discrete ϕ Laplacian operators

... The study of the φ-Laplacian equation is a classical topic that has attracted the atten- tion of many researchers because of its interest for applications. Usually, a φ-Laplacian operator is said to be ... See full document

... In this paper, we consider a kind of Sturm-Liouville boundary value problems with impulsive effects. By using the mountain pass theorem and Ekeland’s variational principle, the existence of two ... See full document

... initial value problems, the existence and multiplicity of solutions were discussed in [, ...fractional boundary value problems (BVPs for short), Agarwal et ... See full document

... analogous problems for both discrete and continuous dynamic systems ...a boundary value problem on a time scale which is neither discrete nor ... See full document

... Recently, boundary value problems (BVPs for short) for fractional differential equa- tions at nonresonance have been studied in many papers (see ... See full document

... Semipositone problems arise in bulking of mechanical systems, design of suspension bridges, chemical reactions, astrophysics, combustion, and management of natural ... See full document

... Our approach will depend on the nature of the kernel of L. If L is invertible we establish conditions for the solvability of (7) by finding a fixed point of the map L −1 F . When L is not invertible, the situation ... See full document

... Differential equations involving the p-Laplacian operator and its generalization, the so- called Φ-Laplacian, have been widely studied due to several applications in various sci- ences. Indeed, many models ... See full document

... According to the related literature [–], a φ-Laplacian operator is said to be singular when the domain of φ is finite (i.e., a < + ∞ ), on the contrary the operator is called reg- ular. On the other hand, we ... See full document

... In the recent years, fractional differential equations played an important role in many fields such as physics, electrical circuits, biology, control theory, etc. (see [–]). Thus, many scholars have paid more attention ... See full document

... A boundary value problem is said to be a resonance one if the corresponding homoge- neous boundary value problem has a non-trivial ...of problems when the differential operator is ... See full document

... The next part of our paper is divided into two sections. Section 2 is devoted to the auxiliary regular problem 1.12, 1.2. We prove the solvability of this problem by the existence principle in 11 and investigate ... See full document

... two-point boundary value prob- lem at nonresonance, and Bai (see []) considered a m-point boundary value problem at ...fractional boundary value problems, see [–] and ... See full document

... A boundary value problem is said to be a resonance one if the corresponding homoge- neous boundary value problem has a non-trivial ...Resonance problems can be expressed as an abstract ... See full document

... the solvability of singular boundary value problems with general differential operators were also investigated in [], where the results on the existence of solutions do not involve the ... See full document

... nonlinear discrete prob- lems subject to various boundary value conditions have been widely studied by using dif- ferent methods (see, ...Neumann boundary value ...a discrete two ... See full document

... For discrete φ-Laplacian problems, there are fewer study results than for differential φ- Laplacian problems. See Cabda [], Cabada and Espinar [] and Bondar []. To the best of our ... See full document

... (.) is degenerate to the Neumann problem, which was studied in [–]. However, as far as we know, there is very little work on the existence of solutions of difference equation with nonlinear boundary ... See full document

... For discrete φ-Laplacian problems, there are less study results than differential φ- Laplacian ...], some existence results were established by the upper and lower solutions ... See full document

... However, this tool cannot be directly used to deal with the quasilinear problem (1.2). To prove Theorems 1.1 and 1.2, we have to construct an equivalent fixed point problem for (1.2); see Proposition 2.2. This is ... See full document