Nonlinear Kirchhoff-Carrier wave equation in a unit membrane with mixed homogeneous boundary conditions.
On the nonexistence of positive solution of some singular nonlinear integral equations.
Existence and asymptotic expansion of solutions to a nonlinear wave equation with a memory condition at the boundary.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value.
On a shock problem involving a nonlinear viscoelastic bar.
On a high-order iterative scheme for a nonlinear Love equation
In this paper, a high-order iterative scheme is established for a nonlinear Love equation associated with homogeneous Dirichlet boundary conditions. This is a development based on recent results (L. T. P. Ngoc, N. T. Long (2011); L. X. Truong, L. T. P. Ngoc, N. T. Long (2009)) to get a convergent sequence at a rate of order to a local unique weak solution of the above mentioned equation.
Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions
In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...
Note on the Carleman's inequality for a negative power number.
On a system of nonlinear wave equations with the Kirchhoff-Carrier and Balakrishnan-Taylor terms
We study a system of nonlinear wave equations of the Kirchhoff-Carrier type containing a variant of the Balakrishnan-Taylor damping in nonlinear terms. By the linearization method together with the Faedo-Galerkin method, we prove the local existence and uniqueness of a weak solution. On the other hand, by constructing a suitable Lyapunov functional, a sufficient condition is also established to obtain the exponential decay of weak solutions.
A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set.
On a fixed point theorem of Krasnosel'skii type and application to integral equations.
Positive solutions for an m-point boundary-value problem.
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