Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems.
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 some nonlinear elliptic systems on the half space.
Existence of solutions for an eigenvalue problem with weight.
Existence of solutions to singular elliptic equations with convection terms via the Galerkin method.
Existence of weak solutions for a nonlinear elliptic system.
Existence of weak solutions for degenerate semilinear elliptic equations in unbounded domains.
Generalized n-Laplacian: boundedness of weak solutions to the Dirichlet problem with nonlinearity in the critical growth range
Let n ≥ 2 and let Ω ⊂ ℝn be an open set. We prove the boundedness of weak solutions to the problem where ϕ is a Young function such that the space W 01 L Φ(Ω) is embedded into an exponential or multiple exponential Orlicz space, the nonlinearity f(x, t) has the corresponding critical growth, V(x) is a continuous potential, h ∈ L Φ(Ω) is a non-trivial continuous function and µ ≥ 0 is a small parameter. We consider two classical cases: the case of Ω being an open bounded set and the case of Ω =...
Hardy–Sobolev critical elliptic equations with boundary singularities
Infinitely many solutions for a Robin boundary value problem.
Infinitely many solutions of strongly indefinite semilinear elliptic systems.
Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.
Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators
We deal with maximum principles for a class of linear, degenerate elliptic differential operators of the second order. In particular the Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypothesis on the degeneracy set of the operator. We derive, as consequences of these principles, some generalized maximum principles and an a priori estimate on the solutions of the Dirichlet problem for the linear equation....
Maximun Principle and existence of solutions for elliptic systems involving schrödinger operators
Multilevel correction adaptive finite element method for semilinear elliptic equation
A type of adaptive finite element method is presented for semilinear elliptic problems based on multilevel correction scheme. The main idea of the method is to transform the semilinear elliptic equation into a sequence of linearized boundary value problems on the adaptive partitions and some semilinear elliptic problems on very low dimensional finite element spaces. Hence, solving the semilinear elliptic problem can reach almost the same efficiency as the adaptive method for the associated boundary...
Multiple end solutions to the Allen-Cahn equation in
An entire solution of the Allen-Cahn equation , where is an odd function and has exactly three zeros at and , e.g. , is called a end solution if its nodal set is asymptotic to half lines, and if along each of these half lines the function looks (up to a multiplication by ) like the one dimensional, odd, heteroclinic solution , of . In this paper we present some recent advances in the theory of the multiple end solutions. We begin with the description of the moduli space of such solutions....
Multiple positive solutions for a class of concave-convex semilinear elliptic equations in unbounded domains with sign-changing weights.
Multiple positive solutions of semilinear elliptic problems in exterior domains.
Multiple solutions for a singular semilinear elliptic problems with critical exponent and symmetries.