[PDF] Top 20 Pohozaev-type inequalities and their applications for elliptic equations

... the Pohozaev identities, we establish a kind of inequalities, named Pohozaev-type inequalities, which have the same effects as Pohozaev identities, and then prove some ... See full document

... Remark  There are many positive operators in different concrete Banach spaces. Therefore, putting concrete Banach spaces and concrete positive operators (i.e., pseudo- differential operators or finite or infinite matrices ... See full document

... Beginning with the work of Picone [11], Picone identity has been investigated by many authors. In particular, we refer the reader to Allegretto [2], Kreith [8], Protter [12], Swan- son [13] and the references cited ... See full document

... Multiscale problems arise in many scientific and engineering disciplines. A typical example is the modelling of flow in a porous medium containing a number of low and high permeability embedded in a matrix. Due to the ... See full document

... Gronwall-Bellman inequalities and their various linear and nonlinear generalizations play very important roles in the discussion of existence, uniqueness, continuation, boundedness, and stability properties of ... See full document

... Since Lyapunov’s study, because the inequality of (.) plays a key role for the qualitative properties, such as oscillatory and disconjugacy etc., of differential equations’ solutions, several authors focused on ... See full document

... value of its derivative is given. This problem has applications in transonic gas dynamics []. The Gellerstedt problem and related problems for mixed elliptic-hyperbolic equations were studied in the ... See full document

... Gronwall-Bellman-Ou-Iang type integral inequalities with two variables. These inequalities generalize former results and can be used as handy tools to study the qualitative as well as the ... See full document

... the inequalities of the Volterra type are used to study the behaviour properties of the solutions to boundary value prob- lems for various types of hyperbolic ...integral equations based on the ... See full document

... where μ > , λ > , and  < β, γ ≤ . Our proposed method can avoid the so-called ‘q-condition,’ and under a new assumption, the more concise results are derived. More- over, to show the application of the more ... See full document

... The concept of generalized eigenvalues was introduced by Protter [] for a system of lin- ear elliptic operators. The first work dealing with generalized eigenvalues for p-Laplacian systems is due to Nápoli and ... See full document

... Gronwall-Bellman type fractional integral inequalities and Volterra-Fredholm type fractional integral inequalities are ...These inequalities provide explicit bounds for unknown ... See full document

... The existence, but not uniqueness, of solutions of the problem (3) with f monotone was studied by Keller [18]. For f ( u ) =  u a with a > 1 , the problem (3) is of interest in the study of the sub-sonic motion of a ... See full document

... The paper is organized as follows: in Section  we recall some results from [] in the special case T = R , used to prove our main results, which are presented in Section . In Section  we give applications of ... See full document

... In recent years, an increasing number of Gronwall inequality generalizations have been discovered to address difficulties encountered in differential equations, cf. [–]. Among these generalizations, we focus on the ... See full document

... Some new Gr¨ uss type discrete inequalities for nonnegative real numbers and applications for the moments of guessing mappings are given.. Integral Inequalities, Gr¨ uss Type Discrete In[r] ... See full document

... Phragmén–Lindelöf inequalities, the underlying system of inequalities is reformulated as a system of smooth equations, and a Schrödinger-type method is proposed to solve it iteratively so that ... See full document

... Recently, Cao et al. [1] derived differential Harnack estimates for positive solutions to (1.1) on Riemannian manifolds with nonnegative Ricci curvature. The idea comes from [7, 8] where a systematic method was developed ... See full document

... ¨ Ozdemir, New inequalities of Hermite-Hadamard type via s-convex functions in the second sense with applications, Appl. Dragomir, On Hadamard-type inequalities involving several kinds o[r] ... See full document

... The new idea is to compute the j–invariants by computing the λ–invariants of the curves. If we know λ then by Theorem 2.5 we can compute j. However, λ is not a random element, instead λ satisfies special properties. For ... See full document