# A perturbation method for multiple sign-changing solutions

## Related Articles

- On Existence of Solution for a Class of Semilinear Elliptic Equations with Nonlinearities That Lies between Different Powers. Alves, Claudianor O.; Souto, Marco A. S. // Abstract & Applied Analysis;2008, p1
We prove that the semilinear elliptic equation -Î”u = f (u), in Î©, u = 0, on âˆ‚Î© has a positive solution when the nonlinearity f belongs to a class which satisfies Î¼tq â‰¤ f (t) â‰¤ Ctp at infinity and behaves like tq near the origin, where 1 < q < (N + 2) / (N - 2) if N...

- Existence of positive solutions of a semilinear nondivergence form elliptic equation in a conical domain. Surnachev, M.; Filimonova, I. // Differential Equations;Jan2007, Vol. 43 Issue 1, p147
The article examines the existence or nonexistence of positive solutions of a semilinear nondivergence form of elliptic equation in a conical domain. It is assumed that the coefficients are bounded and measurable and satisfy the condition. Several assertions resulting from the equation as well...

- Second-Order Analysis for Control Constrained Optimal Control Problems of Semilinear Elliptic Systems. Bonnans, J.F. // Applied Mathematics & Optimization;Nov/Dec98, Vol. 38 Issue 3, p303
Abstract. This paper presents a second-order analysis for a simple model optimal control problem of a partial differential equation, namely, a well-posed semilinear elliptic system with constraints on the control variable only. The cost to be mini-mized is a standard quadratic functional....

- On bases from cosines in Lebesgue spaces with variable summability index. Muradov, Togrul; Hashimov, Chingiz // Journal of Inequalities & Applications;1/4/2016, Vol. 2016 Issue 1, p1
In this paper the perturbed system of cosines is considered. Under certain conditions on the summability index $p (\cdot )$ and perturbation, the basicity of this system in Lebesgue spaces $L_{p (\cdot )} (0,\pi )$ with variable summability index $p (\cdot )$ is proved. The obtained results...

- Boundary Feedback Stabilization of Naghdi’s Model. Shu Gen Chai // Acta Mathematica Sinica;Feb2005, Vol. 21 Issue 1, p169
We consider the stabilization of Naghdiâ€™s model by boundary feedbacks where the model has a middle surface of any shape. First, applying the semigroup approach and the regularity of elliptic boundary value problems, we obtain the existence, the uniqueness, and the properties of solutions...

- HÃ¶lder continuity of solutions of an elliptic equation uniformly degenerating on part of the domain. Alkhutov, Yu. A.; Guseinov, S. T. // Differential Equations;Jan2009, Vol. 45 Issue 1, p53
We consider a second-order divergence elliptic equation in a domain D divided by a hyperplane in two parts. The equation is uniformly elliptic in one of these parts and is uniformly degenerate with respect to a small parameter É› in the other. We show that each solution is HÃ¶lder...

- USING PERTURBATION METHODS AND LAPLACE—PADÃ‰ APPROXIMATION TO SOLVE NONLINEAR PROBLEMS. FILOBELLO-NINO, U.; VAZQUEZ-LEAL, H.; KHAN, Y.; YILDIRIM, A.; JIMENEZ-FERNANDEZ, V. M.; HERRERA-MAY, A. L.; CASTANEDA-SHEISSA, R.; CERVANTES-PEREZ, J. // Miskolc Mathematical Notes;2013, Vol. 14 Issue 1, p89
In this paper, the perturbation method and PadÃ© transformation are used to provide an approximate solution of elliptic integrals of the second kind and of complete integrals of the first kind. Besides, we used the obtained results to calculate an analytic expression for the period of a simple...

- Restoration of Periodicity for a Periodic Parabolic System Under Perturbations in the System Conductivity. Lei, L. // Journal of Optimization Theory & Applications;Sep2011, Vol. 150 Issue 3, p580
We study the stability problem for a periodic system under a small perturbation in the system conductivity. We will show that the periodicity can be restored with a control taken from a certain finite-dimensional space. We also give an estimate on the size of the control.

- Singular perturbations generating complexification phenomena for elliptic shells. Béchet, F.; Sanchez-Palencia, E.; Millet, O. // Computational Mechanics;Jan2009, Vol. 43 Issue 2, p207
This paper deals with elliptic shell problems using the Koiter shell model. When the shell is well-inhibited, the limit membrane problem satisfies the Shapiroâ€“Lopatinskii condition and we have a classical singular perturbation problem. In a previous paper, the existence of two kinds of...