Multiple solutions for a fourth-order nonlinear elliptic problem
نویسنده
چکیده
The existence of multiple solutions for a class of fourth-order elliptic equation with respect to the generalized asymptotically linear conditions is established by using the minimax method and Morse theory.
منابع مشابه
On Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کاملExistence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.
متن کاملNON-POLYNOMIAL SPLINE SOLUTIONS FOR SPECIAL NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS
We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...
متن کاملA Fourth Order Nonlinear Elliptic Equation with Jumping Nonlinearity
We investigate the existence of solutions of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition A2u + CAU = bu+ + f in 0, where R is a bounded open set in Rn with smooth boundary and the nonlinearity bu+ crosses eigenvalues of A2 + CA. We also investigate a relation between multiplicity of solutions and source terms of the equation with the nonlinearit...
متن کاملRenormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces
The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega, $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...
متن کامل