Related papers: Global existence and estimates of the solutions to…

A new method is given for proving the global existence of the solution to nonlinear Volterra integral equations. A bound on the solution is derived. The results are based on a nonlinear inequality proved by the author earlier.

This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we…

A combination of some weighted energy estimates is applied for the Cauchy problem of quasilinear wave equations with the standard null conditions in three spatial dimensions. Alternative proofs for global solutions are shown including the…

We consider nonlinear elliptic equations which contains global coupling as a nonlinear term. We classify the existence of all possible positive solutions to this problem.

In this paper, we establish a global $C^2$ estimates to the Neumann problem for a class of fullly nonlinear elliptic equations. By the method of continuity, we establish the existence theorem of $k$-admissible solutions of the Neumann…

Initial boundary value problems for the generalized Benney-Lin equation posed on bounded intervals and on the right half-line were considered. The existence and uniqueness of global regular solutions on arbitrary intervals as well as their…

In this paper, we study the global existence and regularity of H\"older continuous solutions for a series of nonlinear partial differential equations describing nonlinear waves.

A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…

We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…

We consider a semilinear parabolic equation with flux at the boundary governed by a nonlinear memory. We give some conditions for this problem which guarantee global existence of solutions as well as blow up in finite time of all nontrivial…

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…

We provide global gradient estimates for solutions to a general type of nonlinear parabolic equations, possibly in a Riemannian geometry setting. Our result is new in comparison with the existing ones in the literature, in light of the…

We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully…

We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully…

We consider semilinear parabolic equations with nonlinear boundary conditions. We give conditions which guarantee global existence of solutions as well as blow-up in finite time of all solutions with nontrivial initial data. The results…

A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…

In this article, we consider a semilinear pseudo parabolic heat equation with the nonlinearity which is the product of logarithmic and polynomial functions. Here we prove the global existence of solution to the problem for arbitrary…

There is no general existence theorem for solutions for nonlinear difference equations, so we must prove the existence of solutions in accordance with models one by one. In our work, we found theorems for the existence of analytic solutions…

The non-existence of global solutions for semirelativistic equations with non-gauge invariant power type nonlinearity is revisited by a relatively direct way with a pointwise estimate of fractional derivative of some test functions.

In this paper, we establish a priori estimates for a class of fully nonlinear equations with Neumann boundary conditions. By the continuity method, we have obtained the existence theorem for the Neumann problem.