Existence and regularity of entropy solutions for some nonlinear elliptic equations.
Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data
We prove the existence of a renormalized solution for a nonlinear non coercive divergence problem with lower order terms and measure data. In a particular case we also give a uniqueness result.
Existence de maillages optimaux dans les méthodes d'éléments finis
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 solution for a -Laplacian semipositone problem.
Existence of a solution to with a maximal monotone graph in for every given
Existence of entire explosive positive radial solutions of quasilinear elliptic systems.
Existence of entropy solutions for degenerate quasilinear elliptic equations in
In this article, we prove the existence of entropy solutions for the Dirichlet problem where is a bounded open set of , , and .
Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem.
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 many positive nonradial solutions for a superlinear Dirichlet problem on thin annuli.
Existence of multiple principal eigenvalues for some indefinite linear eigenvalue problems
We study the existence of principal eigenvalues for differential operators of second order which are not necessarily in divergence form. We obtain results concerning multiplicity of principal eigenvalues in both the variational and the general case. Our approach uses systematically the Krein-Rutman theorem and fixed point arguments for the spectral radius of some associated problems. We also use a variational characterization for both the self-adjoint and the general case.
Existence of multiple solutions for a -Laplace equation.
Existence of non-negative solutions for nonlinear equations in the semi-positone case.
Existence of nonnegative solutions to positone-type problems in with indefinite weights.
Existence of nontrivial solutions for singular quasilinear equations with sign changing nonlinearity.
Existence of positive and sign-changing solutions for -Laplace equations with potentials in .
Existence of positive bounded solutions of semilinear elliptic problems.
Existence of positive radial solutions for the elliptic equations on an exterior domain
We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩, where , N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and , f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point...
Existence of positive solutions for Dirichlet problems of some singular elliptic equations.