Existence and nonexistence of positive solutions for singular -Laplacian equation in .
Existence and uniqueness for a -Laplacian nonlinear eigenvalue problem.
Existence and uniqueness of generalized solutions to a telegraph equation with an integral boundary condition via Galerkin's method.
Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition.
Existence and upper semicontinuity of uniform attractors in for nonautonomous nonclassical diffusion equations
We prove the existence of uniform attractors in the space for the nonautonomous nonclassical diffusion equation , ε ∈ [0,1]. The upper semicontinuity of the uniform attractors at ε = 0 is also studied.
Existence for the stationary MHD-equations coupled to heat transfer with nonlocal radiation effects
We consider the problem of influencing the motion of an electrically conducting fluid with an applied steady magnetic field. Since the flow is originating from buoyancy, heat transfer has to be included in the model. The stationary system of magnetohydrodynamics is considered, and an approximation of Boussinesq type is used to describe the buoyancy. The heat sources given by the dissipation of current and the viscous friction are not neglected in the fluid. The vessel containing the fluid is embedded...
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 global entropy solutions to a non-strictly hyperbolic system with a source.
Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity.
Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.
Existence of infinitely many weak solutions for some quasilinear $\vec {p}(x)$-elliptic Neumann problems
We consider the following quasilinear Neumann boundary-value problem of the type $$ \begin {cases} -\displaystyle \sum _{i=1}^{N}\frac {\partial }{\partial x_{i}}a_{i}\Big (x,\frac {\partial u}{\partial x_{i}}\Big ) + b(x)|u|^{p_{0}(x)-2}u = f(x,u)+ g(x,u) &\text {in} \ \Omega , \\ \quad \dfrac {\partial u}{\partial \gamma } = 0 &\text {on} \ \partial \Omega . \end {cases} $$ We prove the existence of infinitely many weak solutions for our equation in the anisotropic variable exponent Sobolev...
Existence of multiple solutions for a -Laplace equation.
Existence of positive and sign-changing solutions for -Laplace equations with potentials in .
Existence of solution for nonlinear elliptic equations with unbounded coefficients and data.
Existence of solutions for a class of Kirchhoff type problems in Orlicz-Sobolev spaces
We consider Kirchhoff type problems of the form ⎧ -M(ρ(u))(div(a(|∇u|)∇u) - a(|u|)u) = K(x)f(u) in Ω ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω where , N ≥ 3, is a smooth bounded domain, ν is the outward unit normal to ∂Ω, , M: [0,∞) → ℝ is a continuous function, , and f: ℝ → ℝ is a continuous function not satisfying the Ambrosetti-Rabinowitz type condition. Using variational methods, we obtain some existence and multiplicity results.
Existence of solutions for a -Laplacian non-homogeneous equations.
Existence of solutions for -Laplacian equations.
Existence of solutions for quasilinear parabolic equations with nonlocal boundary conditions.
Existence of solutions for the -Laplacian problem with singular term.