Search results for "Linear system"
showing 10 items of 1558 documents
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.
Multiple solutions for a Dirichlet problem with p-Laplacian and set-valued nonlinearity
2008
AbstractThe existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.
Elliptic problems with convection terms in Orlicz spaces
2021
Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.
Radial solutions of Dirichlet problems with concave-convex nonlinearities
2011
Abstract We prove the existence of a double infinite sequence of radial solutions for a Dirichlet concave–convex problem associated with an elliptic equation in a ball of R n . We are interested in relaxing the classical positivity condition on the weights, by allowing the weights to vanish. The idea is to develop a topological method and to use the concept of rotation number. The solutions are characterized by their nodal properties.
Nonlinear Potential Theory and PDEs
1994
We consider equations like — div(∣∇u∣ p-2∇u) = µ, where µ is a nonnegative Radon measure and 1 < p < ∞. Results that relate the solution u and the measure µ are reviewed. A link between potential estimates and the boundary regularity of the Dirichlet problem is established.
Existence and uniqueness of a solution for a parabolic quasilinear problem for linear growth functionals with $L^1$ data
2002
We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove uniqueness and a comparison principle in $L^1$ for these solutions. To prove the existence we use the nonlinear semigroup theory.
Multiple solutions with sign information for a (p,2)-equation with combined nonlinearities
2020
Abstract We consider a parametric nonlinear Dirichlet problem driven by the sum of a p -Laplacian and of a Laplacian (a ( p , 2 ) -equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is ( p − 1 ) -superlinear (convex term) and a perturbation which is ( p − 1 ) -sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical p…
On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data
2007
We establish Holder continuity of generalized solutions of the Dirichlet problem, associated to a degenerate nonlinear fourth-order equation in an open bounded set , with data, on the subsets of where the behavior of weights and of the data is regular enough.
A sharp estimate of the extinction time for the mean curvature flow
2007
We establish a pointwise comparison result for a nonlinear degenerate elliptic Dirichlet problem using an isoperimetric inequality involving the total mean curvature. In particular this result provides a sharp estimate for the extinction time of a class of compact surfaces, wider than the convex one, moving by mean curvature flow. Finally we present numerical experiments to compare our estimate with those known in literature.
Positive solutions for parametric singular Dirichlet(p,q)-equations
2020
Abstract We consider a nonlinear elliptic Dirichlet problem driven by the ( p , q ) -Laplacian and a reaction consisting of a parametric singular term plus a Caratheodory perturbation f ( z , x ) which is ( p − 1 ) -linear as x → + ∞ . First we prove a bifurcation-type theorem describing in an exact way the changes in the set of positive solutions as the parameter λ > 0 moves. Subsequently, we focus on the solution multifunction and prove its continuity properties. Finally we prove the existence of a smallest (minimal) solution u λ ∗ and investigate the monotonicity and continuity properties of the map λ → u λ ∗ .