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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 $l i m_{λ \to 0 ⁺} | | u_{λ} | | = 0$ .

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Bemerkungen über nichtlineare Störungen von Schrödinger Operatoren.

Bifurcation and symmetry in problems of capillary-gravity waves.

Bifurcation and symmetry-breaking.

Bifurcation for second-order Hamiltonian systems with periodic boundary conditions.

Bifurcation for the solutions of equations involving set valued mappings.

Bifurcation from the spectrum towards regular values.

Bifurcation into gaps in the essential spectrum.

Bifurcation of free vibrations for completely resonant wave equations

Bifurcation of nonlinear elliptic system from the first eigenvalue.

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

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

Bifurcation results for a class of perturbed Fredholm maps.

Bifurcation theorems for nonlinear problems with lack of compactness

Block iterative methods for a finite family of relatively nonexpansive mappings in Banach spaces.

Book review. Fučík, S., Nečas, J., Souček, J., Souček, V.: Spectral Analysis of Nonlinear Operators

Book review. [Theory of nonlinear operators]

Boundary value problems in weighted spaces

Boundary value problems on [a,b) and singular perturbations

Boundary value problems with nonlinearities having infinite jumps

Bounded solutions of nonlinear Cauchy problems.

Currently displaying 1 – 20 of 27