Search results for " solution"
showing 10 items of 3084 documents
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]).
Three solutions for a perturbed Dirichlet problem
2008
Abstract In this paper we prove the existence of at least three distinct solutions to the following perturbed Dirichlet problem: { − Δ u = f ( x , u ) + λ g ( x , u ) in Ω u = 0 on ∂ Ω , where Ω ⊂ R N is an open bounded set with smooth boundary ∂ Ω and λ ∈ R . Under very mild conditions on g and some assumptions on the behaviour of the potential of f at 0 and + ∞ , our result assures the existence of at least three distinct solutions to the above problem for λ small enough. Moreover such solutions belong to a ball of the space W 0 1 , 2 ( Ω ) centered in the origin and with radius not dependent on 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.
Multiple positive solutions for singularly perturbed elliptic problems in exterior domains
2003
Abstract The equation − e 2 Δ u + a e ( x ) u = u p −1 with boundary Dirichlet zero data is considered in an exterior domain Ω = R N ⧹ ω ( ω bounded and N ⩾2). Under the assumption that a e ⩾ a 0 >0 concentrates round a point of Ω as e →0, that p >2 and p N /( N −2) when N ⩾3, the existence of at least three positive distinct solutions is proved.
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.
Nonlinear Diffusion in Transparent Media
2021
Abstract We consider a prototypical nonlinear parabolic equation whose flux has three distinguished features: it is nonlinear with respect to both the unknown and its gradient, it is homogeneous, and it depends only on the direction of the gradient. For such equation, we obtain existence and uniqueness of entropy solutions to the Dirichlet problem, the homogeneous Neumann problem, and the Cauchy problem. Qualitative properties of solutions, such as finite speed of propagation and the occurrence of waiting-time phenomena, with sharp bounds, are shown. We also discuss the formation of jump discontinuities both at the boundary of the solutions’ support and in the bulk.