The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations.
The effect of variational framework on the spectral asymptotics for nonlinear elliptic two-parameter problems
The exact asymptotic behaviour of the unique solution to a singular Dirichlet problem.
The exterior Dirichlet problem for quasi linear elliptic equations with small boundary data.
The finite element method for nonlinear elliptic equations with discontinuous coefficients.
The first boundary problem for a degenerate elliptic system.
The first eigenvalue for the -Laplacian operator.
The generalized Conley index and multiple solutions of semilinear elliptic problems.
The generalized Dirichlet problem for equations of Monge-Ampère type
The gradient method for non-differentiable operators in product Hilbert spaces and applications to elliptic systems of quasilinear differential equations.
The heat radiation problem: three-dimensional analysis for arbitrary enclosure geometries.
The homogeneous Dirichlet problem for non-elliptic partial differential equations with strong nonlinearities
The Indicatrix Method in Free Boundary Problems.
The interface crack with Coulomb friction between two bonded dissimilar elastic media
We study a model of interfacial crack between two bonded dissimilar linearized elastic media. The Coulomb friction law and non-penetration condition are assumed to hold on the whole crack surface. We define a weak formulation of the problem in the primal form and get the equivalent primal-dual formulation. Then we state the existence theorem of the solution. Further, by means of Goursat-Kolosov-Muskhelishvili stress functions we derive convergent expansions of the solution near the crack tip.
The Lazer-McKenna conjecture for radial solutions in the ball.
The maximum principle for equations with composite coefficients.
The method of fictitious domains in the Signorini problem.
The multiplicity of solutions and geometry of a nonlinear elliptic equation
Let Ω be a bounded domain in with smooth boundary ∂Ω and let L denote a second order linear elliptic differential operator and a mapping from into itself with compact inverse, with eigenvalues , each repeated according to its multiplicity, 0 < λ1 < λ2 < λ3 ≤ ... ≤ λi ≤ ... → ∞. We consider a semilinear elliptic Dirichlet problem in Ω, u=0 on ∂ Ω. We assume that , and f is generated by and . We show a relation between the multiplicity of solutions and source terms in the equation....
The Neumann problem for quasilinear differential equations
In this note we prove the existence of extremal solutions of the quasilinear Neumann problem , a.e. on , , in the order interval , where and are respectively a lower and an upper solution of the Neumann problem.
The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues