Non-symmetric low-index solutions for a symmetric boundary value problem
نویسندگان
چکیده
منابع مشابه
Non-symmetric low-index solutions for a symmetric boundary value problem
Abstract. We consider the equation −∆u = wu on a square domain in R, with Dirichlet boundary conditions, where w is a given positive function that is invariant under all (Euclidean) symmetries of the square. This equation is shown to have a solution u, with Morse index 2, that is neither symmetric nor antisymmetric with respect to any nontrivial symmetry of the square. Part of our proof is comp...
متن کاملSome symmetric boundary value problems and non-symmetric solutions
Abstract. We consider the equation −∆u = wf (u) on a symmetric bounded domain in Rn with Dirichlet boundary conditions. Here w is a positive function or measure that is invariant under the (Euclidean) symmetries of the domain. We focus on solutions u that are positive and/or have a low Morse index. Our results are concerned with the existence of non-symmetric solutions and the non-existence of ...
متن کاملTriple Positive Symmetric Solutions for a Lidstone Boundary Value Problem
In this paper, we consider the Lidstone boundary value problem (−1)y = f(y(t)), 0 ≤ t ≤ 1, y(0) = 0 = y(1), 0 ≤ i ≤ m − 1, where f : R→ [0,∞). Growth conditions are imposed on f and inequalities involving the Green’s function for this problem are used which enable us to apply the Leggett-Williams Fixed Point Theorem for cones in ordered Banach spaces. This in turn yields the existence of at lea...
متن کاملEigenvalues and Symmetric Positive Solutions for a Three-point Boundary-value Problem
In this paper, we consider the second-order three-point boundaryvalue problem u′′(t) + f(t, u, u′, u′′) = 0, 0 ≤ t ≤ 1, u(0) = u(1) = αu(η). Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highestorder derivative occurs nonli...
متن کاملPOSITIVE PSEUDO–SYMMETRIC SOLUTIONS FOR A NONLOCAL p–LAPLACIAN BOUNDARY VALUE PROBLEM
This paper is devoted to the study of the following nonlocal p -Laplacian functional differential equation −φp(x′(t)) )′ = λ f (t,x(t),x ′ (t)) (∫ 1 0 f (s,x(s),x′ (s))ds )n , 0 < t < 1, subject to multi point boundary conditions. We obtain some results on the existence of at least one (when n ∈ Z+ ) or triple (when n = 0) pseudo-symmetric positive solutions by using fixedpoint theory in cone. ...
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: Journal of Differential Equations
سال: 2012
ISSN: 0022-0396
DOI: 10.1016/j.jde.2011.08.014