# Dirichlet problem with indefinite nonlinearities

## Related Articles

- NONTRIVIAL SOLUTIONS FOR KIRCHHOFF TYPE EQUATIONS VIA MORSE THEORY. JIJIANG SUN; SHIWANG MA // Communications on Pure & Applied Analysis;Mar2014, Vol. 13 Issue 2, p483
In this paper, the existence of nontrivial solutions is obtained for a class of Kirchhoff type problems with Dirichlet boundary conditions by computing the critical groups and Morse theory.

- On a resonant-superlinear elliptic problem. Cuesta, Mabel; de Figueiredo, Djairo G.; Srikanth, P.N. // Calculus of Variations & Partial Differential Equations;Jul2003, Vol. 17 Issue 3, p221
We start by discussing the solvability of the following superlinear problem ... where 1 < p < ... , O ? RN is a smooth bounded domain and f satisfies a one-sided Landesman-Lazer condition. We also consider systems of semilinear elliptic equations with nonlinearities of the above form, so...

- AN APPLICATION OF THE LYAPUNOV-SCHMIDT METHOD TO SEMILINEAR ELLIPTIC PROBLEMS. Quố C Anh Ngô // Electronic Journal of Differential Equations;2005, Vol. 2005, p1
In this paper we consider the existence of nonzero solutions for the undecoupling elliptic system -Î”u = Î»u + Î´v + f(u, v), -Î”v = Î¸u + Î³v + g(u, v), on a bounded domain of â„n, with zero Dirichlet boundary conditions. We use the Lyapunov-Schmidt method and the fixed-point...

- AN EXISTENCE RESULT OF ONE NONTRIVIAL SOLUTION FOR TWO POINT BOUNDARY VALUE PROBLEMS. BONANNO, GABRIELE; SCIAMMETTA, ANGELA // Bulletin of the Australian Mathematical Society;Oct2011, Vol. 84 Issue 2, p288
Existence results of positive solutions for a two point boundary value problem are established. No asymptotic condition on the nonlinear term either at zero or at infinity is required. A classical result of Erbe and Wang is improved. The approach is based on variational methods.

- AN EXISTENCE RESULT FOR ELLIPTIC PROBLEMS WITH SINGULAR CRITICAL GROWTH. Nasri, Yasmina // Electronic Journal of Differential Equations;2007, Vol. 2007, p1
We prove the existence of nontrivial solutions for the singular critical problem -Î”u - Âµ/u|x|Â² = Î»f(x)u + u2*-1 with Dirichlet boundary conditions. Here the domain is a smooth bounded subset of â„NN, N â‰¥ 3, and 2* = 2N/N-2 which is the critical Sobolev exponent.

- MULTIPLE SOLUTIONS FOR SYSTEMS OF MULTI-POINT BOUNDARY VALUE PROBLEMS. Graef, John R.; Heidarkhani, Shapour; Lingju Kong // Opuscula Mathematica;2013, Vol. 33 Issue 2, p293
In this paper, we establish the existence of at least three solutions of the multi-point boundary value system ... The approaches used are based on variational methods and critical point theory.

- Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems. Jianmin Guo; Caixia Guo // Discrete Dynamics in Nature & Society;2011, Special section p1
By using Morse theory, the critical point theory, and the character of K1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem -Î” Â² x(k -1) = f(k, x(k)), k âˆˆ â„¤(1, T) subject to x(0) = 0 =...

- Multiple Solutions for the Discrete p-Laplacian Boundary Value Problems. Yuhua Long; Haiping Shi // Discrete Dynamics in Nature & Society;2014, p1
By employing a critical point theorem, established by Bonanno, we prove the existence of three distinct solutions to boundary value problems of nonlinear difference equations with a discrete p-Laplacian operator. To demonstrate the applicability of our results, we also present an example.

- A NOTE ON CRITICAL POINT AND BLOW-UP RATES FOR SINGULAR AND DEGENERATE PARABOLIC EQUATIONS. LIU, B.; LI, F. // Bulletin of the Iranian Mathematical Society;Oct/Nov2015, Vol. 41 Issue 5, p1195
In this paper, we consider singular and degenerate parabolic equations ut = (xÎ± ux)x + um(x0, t) vn(x0, t), vt = (xÎ² vx)x + uq(x0, t)vp(x0, t), in (0, a) Ã— (0, T), subject to null Dirichlet boundary conditions, where m, n, p, q â‰¥ 0, Î±,Î² âˆˆ [0, 2) and x0 âˆˆ (0, a)....