An elliptic equation with no monotonicity condition on the nonlinearity
نویسندگان
چکیده
منابع مشابه
An Elliptic Equation with No Monotonicity Condition on the Nonlinearity
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was o...
متن کاملRupture Solutions of an Elliptic Equation with a Singular Nonlinearity
We construct infinitely many non-radial rupture solutions of the equation ∆u = 1 up in RN\{0}, u(0) = 0, N ≥ 3 with p > pc(N − 1) := N − 1− 2 √ N − 2 2 √ N − 2− (N − 5) .
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 کاملOn the Solvability of a Resonant Elliptic Equation with Asymmetric Nonlinearity
(1.1) −∆u = αu − βu− + g(x, u), u ∈ H 0 (Ω), where α, β are real parameters and u = max{u, 0}, u− = u − u. Without loss of generality, we assume β ≤ α. In fact, denoting by (λi) the increasing sequence of eigenvalues of (−∆,H 0 (Ω)), we study the case where λ1 < β < α and [β, α] intersects this linear spectrum. Here g : Ω×R → R is a Carathéodory function with subcritical growth at infinity, nam...
متن کاملNumerical solution of nonlinear elliptic equation with nonlocal condition ∗
Regimantas Čiupaila, Mifodijus Sapagovas, Olga Štikonienė Vilnius Gediminas Technical University Saulėtekio ave. 11, LT-10223 Vilnius, Lithuania [email protected] Institute of Mathematics and Informatics, Vilnius University Akademijos str. 4, LT-08663 Vilnius, Lithuania [email protected] Vilnius University Naugarduko str. 24, LT-03225 Vilnius, Lithuania olga.stikoniene@mif...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2006
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv:2006022