[PDF] Top 20 Existence of Solutions for Some p(x) polyharmonic Elliptic Kirchhoff Equations

... usual p -Laplacian for s = 1 . Kratochvl and Necâs intro- duced the p -biharmonic operator in [1] [2] [3] to study the physical equations, the p -biharmonic operator for s = 2 and the ... See full document

... The above problem for the case m = 1 has been studied before for existence of solu- tions by many authors. Tarantello in [19] considered the problem for ε f (x) = 1, then he showed that for the limiting ... See full document

... lower solutions, we show the existence of a solution to problem ...provide some asymptotic boundary estimates under appropriate condi- tions on b(x) and ... See full document

... where f is a continuous function. For example, Perera and Zhang [] derived nontrivial solutions for problem (.) with the help of the Yang index and critical groups. In [], Chen et al., by employing fibering map ... See full document

... the existence of multiple solutions for a quasilinear system in- volving a pair of (p(x), q(x))-Laplacian ...multiple solutions for a class of differential inclusion systems ... See full document

... the existence of infinitely many distinct homoclinic radially symmetric solutions whose W 1,p(x) ( R N )-norms tend to zero (to infinity, respectively) under weaker hypotheses about ... See full document

... the existence of three solutions of problem ...the existence of an open interval ⊂ [, + ∞ ) and a positive real number ρ such that, for each λ ∈ , problem ...weak solutions whose norms in ... See full document

... |t| p(x)– with a continuous function p : → (, ∞) and f : R × × R × R N → R satisfies a Carathéodory ...When p(x) is a constant function, the existence of an unbounded branch of ... See full document

... potential V (x), which was firstly introduced in [] and is used to overcome the lack of compactness of embedding of the working space. In other words, under the weaker con- dition (V), the Sobolev embedding is ... See full document

... with p(x,t) growth conditions. We prove the existence and uniqueness of bounded solutions to such a problem, with less constraint to ... See full document

... began to attract the attention of several researchers only after Lion [] had proposed an abstract framework for this problem. Perera and Zhang [] obtained a nontrivial solution of () by using the Yang index and ... See full document

... differential equations arise in the study of deflections of elastic beams on nonlinear elastic ...the existence of solutions of p- biharmonic equations has been studied by several ... See full document

... the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary ...| p in a ball with p > ... See full document

... differential equations have been extensively studied by many researchers due to their various applications in science and engineering ...the equations including both left and right fractional derivative have ... See full document

... a p-Laplacian elliptic equation with Hardy term and Hardy-Sobolev critical exponent, where the nonlinearity is (p – 1)-sublinear near zero and (p ∗ (s) – 1)-sublinear near infinity (p ∗ ... See full document

... < p < ...when p(τ + ) < q < m < p ∗ = N pN –p ...the existence of solutions for ...when p < q < p(τ + ) and μ = ? This is a interesting ... See full document

... the existence of at least one solution, or multiple solutions, or even infinitely many solu- tions for fourth-order boundary value problems using lower and upper solution methods, Morse theory, the ... See full document

... The Kirchhoff-type equation and system have a broad background in phase transitions, population dynamics, mathematical finance, etc. There have been a lot of excellent results related to the existence and ... See full document

... the Kirchhoff equations and the Kirchhoff systems have been considered by variational method in the case involving the p − Laplacian operator [4, 7, 8, 18, 19, ...differential equations ... See full document

... the above theorem? Obviously, this case is resonance. But, this problem is not easy because we face the difficulties of verifying that the energy functional satisfies the (PS) condition if we still follow the idea of []. ... See full document