[PDF] Top 20 Multiple solutions for a fourth-order nonlinear elliptic problem

... This fourth-order semilinear elliptic problem can be considered as an analogue of a class of second-order problems which have been studied by many ...two solutions by a variation ... See full document

... the L p () norm and E = H  () ∩ H   (). The aim of this paper is to prove a multiplicity theorem for problem () when the nonlinearity term f (x, t) exhibits an asymmetric be- havior as t ∈ R approaches +∞ and ... See full document

... The first author is supported by the project of ‘Min-Hong Kong cooperation postdoctoral training’ funded by Fujian Provincial Civil Service Bureau and the Nonlinear Analysis Innovation Team (IRTL1206) funded by ... See full document

... positive solutions for a fourth-order system of integral boundary value problem on time ...of multiple positive solutions for the system is obtained by using the fixed point ... See full document

... linear fourth-order dynamic boundary value problem on time scales and obtains the existence result of positive solutions to a nonlinear fourth-order dynamic boundary value ... See full document

... not require F(x, u, v) → + ∞ as | u | + | v | → + ∞ . With novel growth conditions on F(x,u, v), we develop a new method to check the Cerami compactness condition. Through arguments of critical point theory, we prove the ... See full document

... positive solutions to boundary-value prob- lems for higher order differential equation is observed, see for example ...on nonlinear boundary-value problem for fourth order ... See full document

... The rest of this paper is organized as follows, In Section 2, we present some definitions and back- ground results. For sake of convenience, we also state the fixed point theorems. In Section 3, we construct the Green’s ... See full document

... author got a nontrivial solution of (1.2). In [8], Zhang and Tang also considered the prob- lem (1.2) under the assumption (V), and they obtained infinitely many high energy solu- tions of the problem (1.2). In ... See full document

... The existence of multiple solutions for Neumann problems like those in the form of 1.1 has been studied by a number of authors, such as, for example, the authors of 12–15, and homogeneous Neumann boundary ... See full document

... of multiple positive solutions of a fourth-order differential equation subject to nonlocal and nonlinear boundary conditions that models a particular stationary state of an elastic beam ... See full document

... arises in many applications from mathematical physics, which is usually used to describe some phenomena appearing in various physical, engineering, and other sciences. In [, ], Lazer and Mckenna firstly proposed and ... See full document

... In the last few years, variational methods and critical point theory have been used to study the existence and multiple solutions of discrete boundary value problems. In this article, we utilize this ... See full document

... of multiple nontrivial solutions for some fourth order problems [18, ...the fourth-order equation and the variable exponent equation goes to the p(x)-biharmonic ... See full document

... weak solutions for some fourth order elliptic boundary value problem with bounded nonlinear term decaying at the ...the fourth order elliptic problem ... See full document

... two solutions for a more general nonlinearity g(·, ...nontrivial solutions and four non- trivial solutions by a similar variational approach, depending on the position of a suitable parameter with ... See full document

... The assumed conditions and known results of the theory of monotone operators allow us to prove existence of generalized solutions of the Dirichlet problem associated to our operator (see, e.g., [1]), ... See full document

... Fourth-order nonlinear differential equations have many applications such as balancing condition of an elastic beam which may be described by nonlinear fourth-order ordinary ... See full document

... the problem (1.1) cannot transform into a system of second-order equation, the treat- ment method of second-order system does not apply to the problem ...positive solutions of the ... See full document

... The article is organized as follows: Section 2 is devoted to giving the main result and proving the existence of nontrivial solution of Equation (1). In Section 3, we deal with the multiplicity results of Equation (1) ... See full document