TITLE

Multiple Solutions for a Fourth–order Asymptotically Linear Elliptic Problem

AUTHOR(S)
Ai Qian; Shu Li
PUB. DATE
July 2006
SOURCE
Acta Mathematica Sinica;Jul2006, Vol. 22 Issue 4, p1121
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Under simple conditions, we prove the existence of three solutions for a fourth–order asymptotically linear elliptic boundary value problem. For the resonance case at infinity, we do not need to assume any more conditions to ensure the boundedness of the (PS) sequence of the corresponding functional.
ACCESSION #
21690494

 

Related Articles

  • On the Convergence Rate of the Finite-Difference Solution of a Nonlocal Boundary Value Problem for a Second-Order Elliptic Equation. Berikelashvili, G. K. // Differential Equations;Jul2003, Vol. 39 Issue 7, p945 

    Consider a nonlocal Bitsadze-Samarskii boundary value problem for a second-order elliptic equation with constant coefficients in the unit square omega. Examination of the corresponding difference scheme in weighted Sobolev spaces; Estimation of the convergence rate; Method used to estimate the...

  • Multiple Positive Solutions of Nonhomogeneous Elliptic Equations in Unbounded Domains. Tsing-San Hsu // Abstract & Applied Analysis;2007, p1 

    We will show that under suitable conditions on f and h, there exists a positive number χ* such that the nonhomogeneous elliptic equation -Δu + u = χ*( f (x,u) + h(x)) in Ω, u εH0¹ (Ω), N ≥ 2, has at least two positive solutions if χ ε (0,χ*), a unique...

  • Boundary Feedback Stabilization of Naghdi’s Model. Shu Gen Chai // Acta Mathematica Sinica;Feb2005, Vol. 21 Issue 1, p169 

    We consider the stabilization of Naghdi’s model by boundary feedbacks where the model has a middle surface of any shape. First, applying the semigroup approach and the regularity of elliptic boundary value problems, we obtain the existence, the uniqueness, and the properties of solutions...

  • The Lazer-McKenna conjecture and a free boundary problem in two dimensions. E. N. Dancer; Shusen Yan // Journal of the London Mathematical Society;Dec2008, Vol. 78 Issue 3, p639 

    We prove that certain super-linear elliptic equations in two dimensions have many solutions when the diffusion is small. We find these solutions by constructing solutions with many sharp peaks. In three or more dimensions, this has already been proved by the authors in Comm. Partial Differential...

  • Maximal Regular Abstract Elliptic Equations and Applications. Shakhmurov, V. B. // Siberian Mathematical Journal;Sep2010, Vol. 51 Issue 5, p935 

    The oblique derivative problem is addressed for an elliptic operator differential equation with variable coefficients in a smooth domain. Several conditions are obtained, guaranteing the maximal regularity, the Fredholm property, and the positivity of this problem in vector-valued L-spaces. The...

  • Bounds in spaces of Morrey under Cordes type conditions. Canale, A. // Journal of Applied Functional Analysis;Jan2008, Vol. 3 Issue 1, p11 

    In the study of boundary value problems for linear elliptic equations in nondivergence form with discontinuous coefficients we consider the class of discontinuity of Cordes type. In particular we state some local and non local a priori bounds for solutions of Dirichlet problem in unbounded...

  • Estimates for the Multiplicative Square Function of Solutions to Nondivergence Elliptic Equations. Rivera-Noriega, Jorge // Abstract & Applied Analysis;2007, p1 

    We prove distributional inequalities that imply the comparability of the Lp norms of the multiplicative square function of u and the nontangential maximal function of log u, where u is a positive solution of a nondivergence elliptic equation. We also give criteria for singularity and mutual...

  • The Method of Fictitious Domains in the Signorini Problem. Stepanov, V. D.; Khludnev, A. M. // Siberian Mathematical Journal;Nov/Dec2003, Vol. 44 Issue 6, p1061 

    We justify the method of fictitious domains for an elliptic equation with nonlinear Signorini boundary conditions. The method makes it possible to construct a family of auxiliary problems defined in a wider domain and possessing the property that their solutions converge in an appropriate sense...

  • Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient. Iturriaga, Leonelo; Lorca, Sebastian // Boundary Value Problems;2007, p1 

    We study the existence of positive solutions for a class of degenerate nonlinear elliptic equations with gradient dependence. For this purpose, we combine a blowup argument, the strong maximum principle, and Liouville-type theorems to obtain a priori estimates.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics