A multiplicity result for the scalar field equation
نویسندگان
چکیده
منابع مشابه
A Multiplicity Result for the Scalar Field Equation
Abstract We obtain N − 1 pairs of nontrivial solutions of the scalar field equation in R under a slow decay condition on the potential, without any symmetry assumptions. To overcome the difficulties arising from the lack of compactness, we use the concentration compactness principle of Lions expressed as a suitable profile decomposition for critical sequences. This is a joint work with Cyril Ti...
متن کاملA dimension-depending multiplicity result for the Schrödinger equation
We consider the Schrödinger equation { −∆u+ V (x)u = λK(x)f(u) in R ; u ∈ H(R ), (Pλ) where N ≥ 2, λ ≥ 0 is a parameter, V,K : R → R are radially symmetric functions, and f : R → R is a continuous function with sublinear growth at infinity. We first prove that for λ small enough no non-zero solution exists for (Pλ), while for λ large enough at least two distinct non-zero radially symmetric solu...
متن کاملA multiplicity result for a semilinear Maxwell type equation
In this paper we look for solutions of the equation δdA = f (〈A,A〉)A in R, where A is a 1-differential form and k ≥ 2. These solutions are critical points of a functional which is strongly degenerate because of the presence of the differential operator δd. We prove that, assuming a suitable convexity condition on the nonlinearity, the equation possesses infinitely many finite energy solutions.
متن کاملMultiplicity result to some Kirchhoff-type biharmonic equation involving exponential growth conditions
In this paper, we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity. Using some variational arguments and exploiting the symmetries of the problem, we establish a multiplicity result giving two nontrivial solutions.
متن کاملExact Multiplicity Result for the Perturbed Scalar Curvature Problem in R N ( N ≥ 3 )
Let D1,2(RN ) denote the closure of C∞ 0 (R N ) in the norm ‖u‖2 D1,2(RN ) = ∫ RN |∇u|2. Let N ≥ 3 and define the constants αN = N(N − 2) and CN = (N(N − 2)) N−2 4 . Let K ∈ C2(RN ). We consider the following problem for ε ≥ 0 : (Pε) ⎪⎨⎪⎩ Find u ∈ D1,2(RN ) solving : −∆u = αN (1 + εK(x))u N+2 N−2 , u > 0 } in RN . We show an exact multiplicity result for (Pε) for all small ε > 0.
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: Advances in Nonlinear Analysis
سال: 2014
ISSN: 2191-950X,2191-9496
DOI: 10.1515/anona-2014-0022