[PDF] Top 20 Multiplicity of solutions for critical singular problems

... kind of problem in a bounded domain or in R N , mainly when the operator involved is the Laplacian or the p-Laplacian with convex ...the singular problem in bounded domains, we refer the reader to [ 8 , 9 ] ... See full document

... u (iv) (x) + f (x, u (x) , u 0 (x) , u 00 (x) , u 000 (x)) = sp (x) (1) 2010 Mathematics Subject Classification. Primary: 34B15; Secondary: 34B18, 47H11. Key words and phrases. Higher order Ambrosetti-Prodi ... See full document

... Sacks Keywords: Mountain pass theorem Second deformation theorem Eigenvalues of p-Laplacian Critical groups Constant sign and nodal solutions Extremal solutions.. We consider a nonlinear[r] ... See full document

... minimal solutions uniformly in λ and determine the critical dimension for this class of ...dimension of the riemannian manifold is below the critical ...branch of minimal ... See full document

... theory of multi-point boundary value problems for ordinary differential equa- tions arise in different areas of applied mathematics and physics, especially in heat conduction [4, 5, 27, 29], the ... See full document

... study of this type of problem is motivated by its various applications, for example, in fluid mechanics, in newtonian fluids, in flow through porous media and in glaciology (see ...elliptic problems ... See full document

... Positive solutions for the p-Laplacian and bounds for its first eigenvalue, submitted for ...positive solutions of nonlocal and nonvariational elliptic problems, Nonlinear ...quasilinear ... See full document

... dynamics of these two limiting problems, with ε = 0, one obtains information on the dynamics for small values of ...approximate solutions on pieces of curves that satisfy some limiting ... See full document

... theory of the critical values of j: Prominent in that theory is the ‘‘mountain pass theorem’’ of Ambrosetti-Rabinowitz [7], which reads as ... See full document

... hand, problems driven by more general p-Laplacian-like operators were investigated by De Napoli-Mariani [9], Duc-Vu [10], Krist´aly-Lisei-Varga [16] (all considering a smooth potential) and by Dabuleanu-Radulescu ... See full document

... analysis of singular boundary value problems and many different techniques have been used or developed in order to deal with three main questions: existence and uniqueness of solutions, ... See full document

... a Singular Monotone Term The main objective of this section is to prove theorem ...use of a well known result on lower and upper solutions, namely theorem ... See full document

... true critical exponent for this ...inequalities of Sobolev (p = 2, a = 0 and b = 0) and Hardy (p = 2, a = 0 and b = ...principle of symmetric criticality and variational methods, we prove that the ... See full document

... type of problem with a discussion on the number of solutions of the boundary value problem was introduced in [1] and since then are known as Ambrosetti-Prodi ...type of discussion to ... See full document

... [1] Ben-Israel, A. and Greville, T.N.E., Generalized inverses: theory and appli- cations, Pure and Applied Mathematics, Wiley-Interscience, New York, 2003. [2] Berman, A. and Plemmons, R.J.,“Cones and iterative methods ... See full document

... equations of the form
u u= jxj 2 D f ...existence of solutions, that is usually cited by authors that worked with this operator - however, in that article the authors work with a parabolic equation ... See full document

... study of fractional boundary value problems has seen a tremendous expansion in recent years motivated by both general theory and physical representations and ...[2,4,7,8]. Of interest to the work ... See full document

... methods of critical point theory can be used to obtain solutions of the boundary value ...methods of critical point theory (smooth and nonsmooth alike) fail and we need to device ... See full document

... result of Brézis and Nirenberg ...existence of two positive solutions for problem (P) with λ = 0, still in bounded ...the singular op- erators, R˘adulescu and Smets [26] treated the case 0 ... See full document

... the critical Sobolev exponent, 0 ≤ λ < Λ ˙ = ((N − 2)/2) 2 and f ∈ L ∞ ...a singular term have attracted great interests during the past several years, ...existence of two nontrivial ... See full document