Search results for "General Mathematics"
showing 10 items of 3795 documents
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.
Existence of three solutions for a quasilinear two point boundary value problem
2002
In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:¶¶ $ \left\{\begin{array}{ll} u'' + \lambda h(u')f(t,\:u) = 0\\ u(0) = u(1) = 0.\\\end{array}\right.\ $ ¶¶Our main tool is a recent three critical points theorem of B. Ricceri ([10]).
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 ∗ .
Positive solutions of Dirichlet and homoclinic type for a class of singular equations
2018
Abstract We study a nonlinear singular boundary value problem and prove that, depending on a relationship between exponents of power terms, the problem has either solutions of Dirichlet type or homoclinic solutions. We make use of shooting techniques and lower and upper solutions.
Weak Solutions for a (p(z), q(z))-Laplacian Dirichlet Problem
2020
We establish the existence of a nontrivial and nonnegative solution for a double phase Dirichlet problem driven by a (p(z); q(z))-Laplacian operator plus a potential term. Our approach is variational, but the reaction term f need not satisfy the usual in such cases Ambrosetti-Rabinowitz condition.
Nonlinear diffusion in transparent media: the resolvent equation
2017
Abstract We consider the partial differential equation u - f = div ( u m ∇ u | ∇ u | ) u-f=\operatornamewithlimits{div}\biggl{(}u^{m}\frac{\nabla u}{|\nabla u|}% \biggr{)} with f nonnegative and bounded and m ∈ ℝ {m\in\mathbb{R}} . We prove existence and uniqueness of solutions for both the Dirichlet problem (with bounded and nonnegative boundary datum) and the homogeneous Neumann problem. Solutions, which a priori belong to a space of truncated bounded variation functions, are shown to have zero jump part with respect to the ℋ N - 1 {{\mathcal{H}}^{N-1}} -Hausdorff measure. Results and proofs extend to more general nonlinearities.
Two positive solutions for a Dirichlet problem with the (p,q)‐Laplacian
2020
The aim of this paper is to prove the existence of two solutions for a nonlinear elliptic problem involving the (p,q) -Laplacian operator. The solutions are obtained by using variational methods and critical points theorems. The positivity of the solutions is shown by applying a generalized version of the strong maximum principle.
Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian
2021
The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.
Existence and comparison results for a singular semilinear elliptic equation with a lower order term
2014
This paper deals with the homogeneous Dirichlet problem for a singular semilinear elliptic equation with a first order term. When the datum is bounded we prove an existence result and we show that any solution can be compared with the solution to a suitable symmetrized problem.
On Noncoercive (p, q)-Equations
2021
We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p - 1)-linear near +/-infinity and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.