On the existence and the regularity of an initial boundary problem of vorticity equation
On the existence of a classical solution of a mixed boundary problem for a second order one-dimensional hyperbolic equation. II.
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the existence of blowing-up solutions for a mean field equation
On the existence of bounded solutions of nonlinear elliptic systems.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the existence of five nontrivial solutions for resonant problems with p-Laplacian
In this paper we study a nonlinear Dirichlet elliptic differential equation driven by the p-Laplacian and with a nonsmooth potential. The hypotheses on the nonsmooth potential allow resonance with respect to the principal eigenvalue λ₁ > 0 of . We prove the existence of five nontrivial smooth solutions, two positive, two negative and the fifth nodal.
On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length
The author examined non-zero -periodic (in time) solutions for a semilinear beam equation under the condition that the period is an irrational multiple of the length. It is shown that for a.e. (in the sense of the Lebesgue measure on ) the solutions do exist provided the right-hand side of the equation is sublinear.
On the existence of global holomorphic solutions of differential equations with complex parameters
On the Existence of Global Smooth Solutions of Certain Semi-Linear Hyperbolic Equations.
On the existence of infinitely many periodic solutions for an equation of a rectangular thin plate
On the existence of multiple positive solutions for a certain class of elliptic problems
We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
On the existence of nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method
The existence of nontrivial solutions is considered for the fractional Schrödinger-Poisson system with double quasi-linear terms: where is the fractional Laplacian for , with and . Under assumptions on and , we prove the existence of positive solutions and negative solutions for the above system by using perturbation method and the mountain pass theorem.
On the existence of periodic solutions of a semilinear wave equation with a superlinear forcing term
On the existence of periodic solutions of an hyperbolic equation in a thin domain
For a nonlinear hyperbolic equation defined in a thin domain we prove the existence of a periodic solution with respect to time both in the non-autonomous and autonomous cases. The methods employed are a combination of those developed by J. K. Hale and G. Raugel and the theory of the topological degree.
On the existence of positive solution for an elliptic equation of Kirchhoff type via Moser iteration method.
On the existence of positive solutions for periodic parabolic sublinear problems.
On the existence of positive solutions of semilinear elliptic equations with Dirichlet boundary conditions.
On the existence of solutions of some non-linear Dirichlet problems
On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients