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We prove existence of small amplitude, 2p/v-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions for any frequency $ω$ belonging to a Cantor-like set of positive measure and for a generic set of nonlinearities. The proof relies on a suitable Lyapunov-Schmidt decomposition and a variant of the Nash-Moser Implicit Function Theorem.

Bifurcation of nonlinear elliptic system from the first eigenvalue.

El Khalil, Abdelouahed, Ouanan, Mohammed, Touzani, Bdelfattah (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent.

Cheng, Yuanji (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Bifurcation of stationary and heteroclinic orbits for parametrized gradient-like flows

Thomas Bartsch (1996)

Banach Center Publications

Bifurcation results for a class of perturbed Fredholm maps.

Benevieri, Pierluigi, Calamai, Alessandro (2008)

Fixed Point Theory and Applications [electronic only]

Bifurcation theorems for nonlinear problems with lack of compactness

Francesca Faraci, Roberto Livrea (2003)

Annales Polonici Mathematici

We deal with a bifurcation result for the Dirichlet problem ⎧ $- Δ_{p} u = μ / {| x |}^{p} {| u |}^{p - 2} u + λ f (x, u)$ a.e. in Ω, ⎨ ⎩ $u_{| \partial Ω} = 0$ . Starting from a weak lower semicontinuity result by E. Montefusco, which allows us to apply a general variational principle by B. Ricceri, we prove that, for μ close to zero, there exists a positive number $λ *_{μ}$ such that for every $λ \in] 0, λ *_{μ} [$ the above problem admits a nonzero weak solution $u_{λ}$ in $W ₀^{1, p} (Ω)$ satisfying $l i m_{λ \to 0 ⁺} | | u_{λ} | | = 0$ .

Bijectivity of *-Endomorphisms of ...(H) and the Unilateral Shift.

Lajos Molnár (1996)

Monatshefte für Mathematik

Bilinear Expansions of the Kernels of Some Nonselfadjoint Integral Operators

Milutin Dostanić (2001)

Matematički Vesnik

Bilinear expansions of the kernels of some nonselfadjoint integral operators.

Dostanić, Milutin (2001)

Matematichki Vesnik

Bilinear forms and nuclearity

Hans Jarchow, Kamil John (1994)

Czechoslovak Mathematical Journal

Bilinear mappings and operator ideals

Braunß, A., Junek, H. (1985)

Proceedings of the 13th Winter School on Abstract Analysis

Bilinear Mappings and Trace Class Ideals.

Andrew M. Tonge (1986)

Mathematische Annalen

Bilinear multipliers on Lorentz spaces

Francisco Villarroya (2008)

Czechoslovak Mathematical Journal

We give one sufficient and two necessary conditions for boundedness between Lebesgue or Lorentz spaces of several classes of bilinear multiplier operators closely connected with the bilinear Hilbert transform.

Bilinear operators associated with Schrödinger operators

Chin-Cheng Lin, Ying-Chieh Lin, Heping Liu, Yu Liu (2011)

Studia Mathematica

Let L = -Δ + V be a Schrödinger operator in $ℝ^{d}$ and $H ¹_{L} (ℝ^{d})$ be the Hardy type space associated to L. We investigate the bilinear operators T⁺ and T¯ defined by $T^{\pm} (f, g) (x) = (T ₁ f) (x) (T ₂ g) (x) \pm (T ₂ f) (x) (T ₁ g) (x)$ , where T₁ and T₂ are Calderón-Zygmund operators related to L. Under some general conditions, we prove that either T⁺ or T¯ is bounded from $L^{p} (ℝ^{d}) \times L^{q} (ℝ^{d})$ to $H ¹_{L} (ℝ^{d})$ for 1 < p,q < ∞ with 1/p + 1/q = 1. Several examples satisfying these conditions are given. We also give a counterexample for which the classical Hardy space estimate fails.

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