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1.
We prove the existence of peak solutions of nonlinear elliptic equations on bounded domains when the diffusion is small. We greatly weaken the non-degeneracy condition usually assumed.  相似文献   

2.
We prove the existence of solutions for a nonlocal equation arising from the mathematical modeling of MicroElectroMechanicalSystems (MEMS). The existence result, obtained within a suitable Implicit Function Theorem framework, is established under rather general boundary conditions and for bounded domains whose diameter is fairly small.  相似文献   

3.
We prove the existence and uniqueness of a solution to the elliptic transmission problem in nonsmooth domains in the weighted Hölder space. The coercive estimates of the solution are given.  相似文献   

4.
In this paper, we deal with a quasilinear elliptic system in exterior domains with dependence on the gradient and coupling of the equations not only inside of the domain, but also on the boundary. We prove the existence of positive, negative or sign changing weak solutions. Our approach relies on an aproximation argument and an adequate elliptic “a priori” estimate.  相似文献   

5.
We extend to the case of many competing densities the results of the paper (Ann. Inst. H. Poincaré 6 (2002)). More precisely, we are concerned with an optimal partition problem in N-dimensional domains related to the method of nonlinear eigenvalues introduced by Nehari, (Acta Math. 105 (1961)). We prove existence of the minimal partition and some extremality conditions. Moreover, in the case of two-dimensional domains we give an asymptotic formula near the multiple intersection points. Finally, we show some connections between the variational problem and the behavior of competing species systems with large interaction.  相似文献   

6.
We prove the existence of a weak solution of the Dirichlet problem for a class of elliptic partial differential systems in separable Orlicz–Sobolev spaces.  相似文献   

7.
We prove the existence of solutions of quasilinear second order elliptic equations with quasilinear Venttsel boundary conditions in both classical and weak sense, under natural structure conditions.  相似文献   

8.
This paper is concerned with maximization and minimization problems of the energy integral associated to p-Laplace equations depending on functions that belong to a class of rearrangements. We prove existence and uniqueness results, and present some features of optimal solutions. The radial case is discussed in detail. We also prove a result of uniqueness for a class of p-Laplace equations under non-standard assumptions.  相似文献   

9.
We consider the Neumann problem for the Hénon equation. We obtain existence results and we analyze the symmetry properties of the ground state solutions. We prove that some symmetry and variational properties can be expressed in terms of eigenvalues of a Steklov problem. Applications are also given to extremals of certain trace inequalities.  相似文献   

10.
We establish the existence of a nontrivial solution to systems of coupled Poisson equations with critical growth in unbounded domains. The proofs rely on a generalized linking theorem due to Krysewski and Szulkin, and on a concentration-compactness argument since the Palais-Smale condition fails at all critical levels.  相似文献   

11.
This paper deals with a class of semilinear elliptic Dirichlet boundary value problems at resonance. We introduce a sufficient Landesman–Lazer condition for the existence of pair positive–negative solutions. Furthermore, developing the fibering method in the framework of the Leray–Schauder degree theory we can prove the existence of branches for positive and negative solutions.  相似文献   

12.
In the present paper we consider the Dirichlet problem in a convex domain for the multidimensional p-Laplace equation with nonlinear source. We prove the existence of the unique continuous viscosity solution under quite general assumptions on the structure of the source. Received: 18 January 2006  相似文献   

13.
We consider a general nonlinear elliptic problem of the second order whose associated functional presents two linking structures and we prove the existence of three nontrivial solutions to the problem.  相似文献   

14.
We prove the existence of solutions to nonlinear free boundary problem with singularities at given points.  相似文献   

15.
In this paper we prove the existence of solutions of nonlinear equations of the type-div(a(x, u, Du)+H(x, u, Du)=f, wherea andH are Caratheodory functions andf is a bounded Radon measure. We remark that the operator can be not coercive. We give also some regularity results.  相似文献   

16.
The aim of this paper is to investigate the Dirichlet problem of prescribed mean curvature equations. We show the existence of a weak solution. The boundary of domains does not always satisfy the H-convexity condition. Our method is not to construct the barrier functions directly, but to use some uniform estimate for solutions of the approximating regularized solutions.  相似文献   

17.
We prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of arbitrary growth. Moreover, if the symmetry of the problem is broken by a small enough perturbation term, we find at least three solutions. The proofs utilise a variational setting given by de Figueiredo and Ruf in order to prove an existence's result and the “algebraic” approach based on the Pohozaev's fibering method.  相似文献   

18.
We prove the existence of classical solutions of elliptic equations of Monge-Ampère type subject to a semilinear oblique boundary condition which is a perturbation of the Neumann boundary condition. Our techniques also allow us to treat fully nonlinear strictly oblique boundary conditions satisfying a concavity condition. Examples show that the above restrictions on the boundary condition are generally necessary for the existence of classical solutions. Received May 22, 1996 / Accepted April 10, 1997  相似文献   

19.
We consider nonlinear elliptic equations driven by the p-Laplacian differential operator. Using degree theoretic arguments based on the degree map for operators of type (S)+ , we prove theorems on the existence of multiple nontrivial solutions of constant sign.  相似文献   

20.
In the present paper, we are concerned with some degenerate quasilinear equations involving variable exponents. Using various (variational and nonvariational) techniques, we prove existence, nonexistence and multiplicity results.  相似文献   

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