Existence of a minimal solution and a maximal solution of a nonlinear elliptic boundary value problem of the fourth order
Existence of a nonautonomous SIR epidemic model with age structure.
Existence of a nonstationary Poiseuille solution.
Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian
In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.
Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent
We consider the following Kirchhoff type problem involving a critical nonlinearity: ⎧ in Ω, ⎨ ⎩ u = 0 on ∂Ω, where (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.
Existence of a positive solution for a -Laplacian semipositone problem.
Existence of a principal eigenvalue for the Tricomi problem.
Existence of a ray of eigenvalues for equations with discontinuous operators.
Existence of a renormalized solution of nonlinear degenerate elliptic problems
We study a general class of nonlinear elliptic problems associated with the differential inclusion in Ω where . The vector field a(·,·) is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in function spaces we prove existence of renormalized solutions for general -data.
Existence of a solution for a class of nonlinear parabolic systems.
Existence of a solution for a nonlinearly elastic plane membrane “under tension”
A justification of the two-dimensional nonlinear “membrane” equations for a plate made of a Saint Venant-Kirchhoff material has been given by Fox et al. [9] by means of the method of formal asymptotic expansions applied to the three-dimensional equations of nonlinear elasticity. This model, which retains the material-frame indifference of the original three dimensional problem in the sense that its energy density is invariant under the rotations of , is equivalent to finding the critical points...
Existence of a solution for the initial boundary value problem for a high order parabolic equation in an unbounded domain.
Existence of a solution of a Fourier nonlocal quasilinear parabolic problem.
Existence of a solution to with a maximal monotone graph in for every given
Existence of absorbing set for a nonlinear wave equation.
Existence of almost automorphic solutions to some classes of nonautonomous higher-order differential equations.
Existence of axisymmetric weak solutions of the 3-D Euler equations for near-vortex-sheet initial data.
Existence of big pieces of graphs for parabolic problems.
Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source
This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.
Existence of blowup solutions for nonlinear problems with a gradient term.